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Solution: Let a number be x Then, 2x = x2 or, x2 - 2x = 0 or, x(x - 2) = 0 so, x = 2 Thus , the number is .....
Let x be the number. Then, x2 + 5 = 30 or, x2 = 25 or, x = (∓5) so the number is + 5 or .....
Let the number be x. According to question, x2/2 - 7= 25 or, x2/2 = 32 or, x2 = 64 or, x2 = 82 or, x = ± 8 so, x = + 8 This is the required .....
Solution : Let the number be x. Then, x2 - 4 = 21 or, x2 = 25 or, x2 = (∓ 5)2 so, the number is +5 or .....
Solution : 5x2 + 8x - 21 = 0 or, 5x2 + 15x - 7x - 21 = 0 or, 5x ( x + 3) - 7 ( x + 3) = 0 or, (5x - 7)(x + 3) = 0 so, x = 7/5 or .....
Solution : x2-3x - 28 = 0 or, x2 - 7x + 4x - 28 = 0 or, x(x-7)+4(x-7) = 0 or, (x-7) (x+4) = 0 So, x = 7 or .....
Solution : x2 - 2x - 8 = 0 or, x2 - 4x + 2x - 8 = 0 or, x ( x - 4) + 2 ( x - 4) = 0 or, ( x - 4 ) ( x + 2) = 0 So, x = 4 or .....
Solution : x2 + 9x + 18 = 0 or, x2 + 6x + 3x + 18 = 0 or, x(x + 6) + 3(x + 6) = 0 or, (x + 6)(x + 3) = 0 So, x = -6 or .....
Solution : x2 - 5x + 6 = 0 or, x2 - 3x - 2x + 6 = 0 or, x ( x - 3 ) - 2 ( x - 3) = 0 or, (x - 3) ( x - 2) = 0 so, x = 3 or .....
Solution : x2 - 3x + 2 = 0 or, x2 - 2x - x + 2 = 0 or, x (x-2) -1(x-2) =0 or, (x-2)(x-1) = 0 so, x = .....
Solution : 8x2 / 3 = 3/2 16x2 = 9 or, x2 = 9/16 or, x2 = (∓3/4)2 or, x = +3/4 or - .....
Solution : x2 / 7 - 7 = 0 or, x2 / 7 = 7 or, x2 = 49 or, x2 = ( ∓ 7 ) 2 Thus, x = + 7 or - .....
Solution : x2 - 25 = 0 or, x2 = (∓ 5)2 so, x = + 5 or - .....
Solution : Let us consider that the second bicycle will meet the first bicycle after x hours. Speed of second bicycle = 30 km/hr i.e. in 1 hour, the second bicycle will cover 30 km. In x hours, the second bus will cover 30x km. Speed of .....
Solution : Let x be the age of father and y be the age of mother. 1st condition : x = 3y .........1 2nd condition : x -20 = y + 10 x - y = 30 ...... 2 From 1 and 2, 3y - y = 30 2y = 30 or, y = 15 and, x = 3 * 15 = .....
Solution : Let x be the age of father and y be the age of son. 1st condition : x + y = 44 .........1 2nd condition : x + 8 = 2 ( y + 8 ) x + 8 = 2y + 16 x - 2y = 8 x = 2y + 8 ...... 2 From 1 and 2, 2y + 8 + y = 44 or, 3y = 44 - 8 = .....
Solution : Let x/y be the required fraction. 1st condition : x = y + 5 ...... 1 2nd condition : x + 1 / y + 1 = 1/2 or, 2x + 2 = y + 1 or, 2x - y = -1 ...... 2 From 1 and 2, 2(y + 5) - y = -1 2y + 10 - y = -1 y = .....
The main objective of establishment of the national human rights commission in Nepal are: 1. To respect, protect and promote human rights and ensure effective enforcement thereof. 2. Inquire on its own initiative or on petition or complaint lodged .....
Solution : Since, n = 4,5,6,7 And 3n-k = 58 or, k = 3n-58 For, n=4, k = 3*4 - 58 = -46 For, n= 5, K = 3*5 - 58 =-43 For, n= 6, K = 3*6 - 58 =-40 For n = 7, K = 3*7 - 58 = .....
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Solution : Let age of mother be x and of daughter be y. 1st condition : 1/6 x = y or, x = 6 y ......1 2nd condition : x - y = 35 ..... 2 From 1 and 2, 6y - y = 35 or, 5 y = 35 or, y = 7 and, x = 6 y = 6 * 7 = 42 years Thus, the age .....
let, present ages: father = x ,& son = y. sum: x+y = 38..........i difference: x-y = 22......ii adding equation i & ii x+y + x-y = 38 .....
Let x and y be the given numbers. 1st condition : 3 ( x + y ) = 42 or, x + y = 14 ......1 2nd condition : 5 ( x - y ) = 20 or, x - y = 4 or, x = y + 4 .....2 from 1 and 2, y + 4 + y = 14 or, 2y + 4 = 14 or, 2y = 10 or, y = 5 and, x = y + .....
solution : let , number be x & y: x˃y from question x = 3y.....i difference: x-y = 12 or, 3y - y = 12 [ using x from .....
solution : let, the one number = x. then, another number = 2x sum : x + 2x = 30 or, 3x = 30 or, x = 30/3 .....
Let two numbers be x and y. First condition : x + y = 60 ....... 1 Second condition : x - y = 10 .......2 from 2, x = y + 10 then , from 1, y + 10 + y = 60 or, 2y + 10 = 60 or, 2y = 50 or, y = 25 and, x = y + 10 = 25 + 10 = 35 so, Two .....
Solution : 10x + y = 7 ( x + y ) or, 10 x + y = 7x + 7y or, 3x - 6y = 0 or, x - 2y = 0 .........1 and, 10x + y - 36 = 10y + x or, 9x - 9y = 36 or, x - y = 4 ......2 Solving 1 and 2, x - 2y = 0 x - y = 4 - + .....
solution: x +y = 5 or, x=5-y .......i 10x+y-9 = 10y + x or, 9x-9y = 9 or,9(x-y) = 9 or,x-y = 1 5- y - y = 1 [ putting value of x from i.] or, -2y = 1-5 .....
solution; x - 20 = 5(y-20) or, x - 20 = 5y -100 or, x = 5y-100+20 = 5y -80........i x - 2y = 10 putting value of x from i. x - 2y = .....
solution; equation: x-y = 30..........i x+5 = 2(y+5) or, x+5 = 2y+ 10 or, .....
Solution : y = 2x - 3 or, 2x - y = 3 ........1 and, 2y + x = 4 or, x + 2y = 4 .....2 Solving 1 and 2, 2x - y = 3 ] * 1 x + 2y = 4 ] * 2 .................... 2x - y = 3 2x + 4y = 8 - .....
Solution : x = 8 - 2y x + 2y = 8 ...1 and, x + y = 6 Solving 1 and 2, x + 2y = 8 x + y = 6 - - - .................. y = 2 and, x + 2y = 8 or, x + 2*2 = 8 or, x = 4 Thus, x .....
Solution : y = x - 2 x - y = 2 ......1 and, x + y = 4 .....2 Then, x + y = 4 x - y = 2 ............... 2x = 6 or, x = 3 and, x + y = 4 or, 3 + y = 4 or, y = 1 Thus, x = 3 and y = .....
1st expression = a3 -1 = (a - 1) (a2 + a +1) 2nd .....
Solution : 1stexpression : a3 - 4 a = a ( a2 - 4 ) = a (a-2)(a+2) 2nd expression : a4 - a3 - 2a2 = a2 ( a2 - a - 2) = a2 ( a2 - 2a+a - 2) =a2 [ a(a-2) + 1(a - 2)] = a2 (a - 2) ( a + 1 ) 3rd expression : a3 - 8 = (a - 2 ) ( a2 + 2a + .....
First expression = x3 - 9x = x ( x2 - 9 ) = x ( x2 - 32 ) = x ( x - 3 ) ( x + 3 ) Second expression = x4 - 2x3 - 3x2 = x2 ( x2 - 2x - 3 ) = x2 ( x2 - 3x + x - 3 ) = x2 { .....
1st expression : x4 - y4 = (x2)2 - (y2)2 = (x2 + y2 ) ( x2 - y 2 ) = ( x2 + y2 ) ( x - y ) ( x + y ) 2nd expression : ( x2 - y 2 ) = ( x - y ) ( x + y ) 3rd expression : x3 - y3 = ( x - y ) ( x2 + xy + y2 .....
First expression : (a-3)2 = (a-3) (a-3) 2nd Expression : a2 - 9 = (a-3) (a+ 3) 3rd expression : a3 + 27 = a3 + 33 = (a+3) (a2 - 3a + 9) So, LCM = (a-3)(a-3) (a+3) (a2 - 3a + 9) = (a+3) (a-3)2 (a2 - 3a .....
Solution : 1st expression : a2 - 4 = (a + 2) ( a - 2) 2nd expression : a3 - 8 = ( a - 2 ) ( a2 + 2a + 4) 3rd expression : (a + 2)2 = (a + 2) ( a + 2) LCM = (a+2) (a - 2 ) (a + 2) ( a2 + 2a + .....
1st expression = a4 + a2b2 + b4 = a4 + b4 + a2b2 = ( a2 )2 + ( b2 )2 + a2b2 = ( a2 + b2 )2 - 2a2b2 + a2b2 = ( a2 + b2 )2 - ( ab )2 = ( a2 + b2 + ab )( .....
1st expression : x4 + x2y2 + y4 = (x2)2 + x2y2 + (y2)2 = ( x2 + y2 )2 - 2x2y2 + x2y2 = ( x2 + y2)2 - x2y2 = ( x2 + y2 ) 2 - (xy)2 = ( x2 + xy + y2 ) ( x2 - xy + y2 ) 2nd expression : x3 - y3 = ( x - y ) (x2 + xy + y2 ) LCM = (x .....
Solution : 1st expression : a4b - ab4 = ab ( a3 - b3 ) = ab ( a - b ) (a2 + ab + b2 ) 2nd expression : a4b2 - a2b4 = a2b2 ( a2 - b2 ) = a2b2 ( a - b ) ( a + b .....
Solution : 1st expression : x2 - 9 = ( x+ 3) ( x - 3 ) 2nd expression : 3x3 + 81 = 3 ( x3 + 27) = 3 ( x + 3 ) (x2 - 3x + 9) HCF = 3 (x + 3) (x - 3 ) (x2 - 3x + 9) = 3 (x2 - 9 ) (x2 - 3x + .....
Solution : 1st expression : a3 - b3 = ( a - b ) ( a2 + ab + b2 ) 2nd expression : a2 + ab + b2 HCF = a2 + ab + .....
Solution : 1st expression : 4x2 - 2x = 2x (2x - 1) 2nd expression : 8x3 - 2x = 2x ( 4x2 - 1) = 2x ( 2x + 1 ) ( 2x - 1 ) HCF = ( 2x - 1 .....
Solution : 1st expression : x3 - 1 = (x-1)(x2 + x + 1) 2nd expression: x4 + x2 + 1 = (x2)2 + (1)2 + x2 = (x2 + 1 )2 - 2x2 + x2 = (x2 + 1 )2 - x2 = (x2 + 1 + x ) (x2 + 1 - x ) = (x2 +x + 1 ) (x2 -x + 1 ) 3rd expression : x3 + 1 + 2x2 + .....
You can notice during the day, the bright object in the sky. It's the Sun, from which we can get heat and light enegy. The sun is the star at the center of the solar system. It is a hot ball of gases that gives off great .....