The difference between the squares of two consecutive numbers is … - Vidyadip

Question

The difference between the squares of two consecutive numbers is 31 . Find the numbers.

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Answer

Let the requierd number $= x$
Then Four-fifth of the number $=x+1$
$\therefore$ According to the condition:
$(x+1)^2-(x)^2=31$
$\Rightarrow x^2+2 x+1-x^2=31$
$\Rightarrow 2 x=31-1=3030$
$\Rightarrow x=\frac{30}{2}=15$
$\therefore$ First number $=15$
And second number = $15+1=16$
Hence numbers are 15, 16
Check: $(16)^2-(15)^2=256-225=31$
Which is given
$\therefore$ Our answer is correct.

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