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The sums of squares of two consecutive positive odd numbers is 290. Find the number.. ​

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493 cents Gregory Peterson
Answer:

The sums of squares of two consecutive positive odd numbers is 290. Find the number.

\huge\bold{\underline{Answer:}}

\green\bigstar Given:

The sums of squares of two consecutive positive odd numbers is 290

\blue\bigstar To find:

Find the number.

\purple\bigstar Solution:

Let the two consecutive number be x and (x+2)

According to question, we have

\sf{:\implies x²+(x+2)²=290}

\sf{:\implies 2x²+4x+4=290}

\sf{:\implies 2x²+4x=290-4}

\sf{:\implies 2x²+4x=286}

\sf{:\implies 2(x²+2x)=286}

\sf{:\implies x²+2x=143}

\sf{:\implies x²+2x-143=0}

\sf{:\implies x²+13x-11x-143=0}

\sf{:\implies x(x+13)-11(x+13)=0}

\sf{:\implies (x+13)(x-11)=0}

\sf{:\implies x=-13}

or,

\boxed{\bf{\pink{⟹\:x=11}}}

Since the number is positive,the number is x = 11

.°. x + 2 = 11 + 2 = 13

Therefore,

sum of numbers is = ( 11 + 13 ) = 24

Therefore, the number is 24

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Gregory Peterson
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