What is the solution please! i need this!!asap!!

Mathematics

1 answer:

Vlad1618 [11]3 years ago

7 0

I believe the answer is no solutions

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Sergio [31]

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3 years ago

The sum of squares of two consecutive odd numbers is 514 find the numbers

amid [387]

Correct Question : The sum of squares of two consecutive positive odd numbers is 514. Find the numbers.

$\rule{130}1$

Solution :

Let the two consecutive positive odd numbers be x and (x + 2)

$\rule{130}1$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf x^2 + (x + 2)^{2} = 514 \\\\\\:\implies\sf x^2 + x^2 + 4x + 4 = 514\\\\\\:\implies\sf 2x^2 + 4x + 4 = 514 \\\\\\:\implies\sf 2x^2 + 4x = 514 - 4\\\\\\:\implies\sf 2x^2 + 4x = 510 \\\\\\:\implies\sf 2x^2 + 4x - 510 = 0\\\\\\:\implies\sf x^2 + 2x - 255 = 0 \:\:\:\:\:\Bigg\lgroup \bf{Dividing\:by\:2}\Bigg\rgroup\\\\\\:\implies\sf x^2 + 17x - 15x - 255 = 0\\\\\\:\implies\sf x(x + 17) - 15(x + 17) = 0\\\\\\:\implies\sf (x + 17) (x - 15)\\\\\\:\implies\sf x = - 17\:or\:x = 15\\\\\\:\implies\underline{\boxed {\sf x = 15}}\:\:\:\:\:\Bigg\lgroup \bf{Positive\:odd\: number}\Bigg\rgroup$