Question

the sum of squares of two consecutive whole numbers is 61. find the numbers​

Answer 1

ans : 5 and 6

5square + 6square

= 25 + 36

= 61

Answer 2

Let the numbers be X and X+1

Their sum is 61, therefore:

${x}^{2} + {(x + 1)}^{2} = 61$

(applying (a+b)^2 formula (= a^2 + b^2 +2ab)

${x}^{2} + {x}^{2} + 1 + 2 \times x \times 1 = 61$

$2 {x}^{2} + 2x = 61 - 1$

Taking 2 common,

$2 ( {x}^{2} + x) = 60$

${x}^{2} + x = 60 \div 2$

${x}^{2} + x = 30$

${x}^{2} + x - 30 = 0$

Factorising ( - 30 (factors equal to -5 and 6)

${x}^{2} + 6x - 5x - 30 = 0$

$x(x + 6) - 5(x + 6)$

$(x - 5)(x + 6) = 0$

Therefore, x-5= 0 and x+6=0

therefore, X=5 and X= -6

Since it's 'whole numbers' (given in question) negative numbers are not considered ( so X is not equal to -6)

therefore x = 5 and X+1 = 6

The numbers are 5 and 6