Question

I have a question that says the product of the squares of two consecutive integers is

256 036. Find the integers. Hint if one integer is x then the other integer can be represented as ( x+1)

Answer 1

Answer:

given,

x*(x+1)=256036

x^2+x=256036

Answer 2

$Let \: x \:and \: (x+1) \:are \: two \: consecutive\\integers .$

/* According to the problem given */

$x^{2} (x+1)^{2} = 256036$

$\implies [ x(x+1)]^{2} = ( 506)^{2}$

$\implies x(x+1) = 506$

$\implies x(x+1) = 22\times 23$

$\implies x(x+1) = 22( 22 + 1 )$

Therefore.,

$\red { Required \:two \: integers \:are } \\\green { (22,23 ) \:or \: (-22,-23) }$

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