Question

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There is question of maths lovers✌


➡The sum of squares of two consecutive positive odd number is 514. find the numbers.

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Answer 1

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Answer 2

$\underline{\underline{\bold{Question:}}}$

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

$\underline{\bold{Solution:}}$

$\boxed{\bold{Difference\:between \:two\:consecutive\:odd\:no.\:will\;be\:always\:2.}}$

$\bold{\textsf{Let the first odd no. be x.}}\\\\\\\bold{\textsf{So second one = (x+2).}}$

According to question,

The sum of squares of two consecutive positive odd number is 514.

$\implies{\bold{x^2+(x+2)^2=514}}\\\\\\\boxed{\bold{(a+b)^2=a^2+2ab+b^2}}\\\\\\\implies{\bold{x^2+x^2+4x+4=514}}\\\\\\\implies{\bold{2x^2+4x-510=0}}\\\\\\\implies{\bold{x^2+2x-255=0}}\\\\\\\implies{\bold{x^2+17x-15x-255=0}}\\\\\\\implies{\bold{x(x+17)-15(x+17)=0}}\\\\\\\implies{\bold{(x+17)(x-15)=0}}\\\\\\\implies{\bold{\left x=\{ {{+15} \atop {-17}} \right. }}\\\\\textsf{\bold{Possible value of x = 15.}}\\\\\\\boxed{\boxed{\bold{\textsf{The odd numbers are 15 and 17.}}}}$