Find two consecutive numbers whose squares have the sum 85. - Vidyadip

Question

Find two consecutive numbers whose squares have the sum $85$.

✓

Answer

Let two consecutive numbers be $X$ and $(x+1)$
Then according to question
$x^2+(x+1)^2=85$
$x^2+x^2+2 x+1=85$
$2 x^2+2 x-85+1=0$
$2 x^2+2 x-84=0$
$x^2+x-42=0$
$x^2+7 x-6 x-42=0$
$x(x+7)-6(x+7)=0$
$(x+7)(x-6)=0$
$(x+7)=0$
$x=-7$
$\text { or }(x-6)=0$
$x=6$
Since, $x$ being a number,
Therefore,
When $x=-7$ then
$x+1=-7+1$
$x+1=-6$
And when $x=6$ then
$x+1=6+1$
$x+1=7$
Thus, two consecutive number be either $6,7$ or $-6,-7$

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