Question

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

Answer 1

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

Answer 2

⟹x²+(x+2)²=290

\sf{:\implies 2x²+4x+4=290}:⟹2x²+4x+4=290

\sf{:\implies 2x²+4x=290-4}:⟹2x²+4x=290−4

\sf{:\implies 2x²+4x=286}:⟹2x²+4x=286

\sf{:\implies 2(x²+2x)=286}:⟹2(x²+2x)=286

\sf{:\implies x²+2x=143}:⟹x²+2x=143

\sf{:\implies x²+2x-143=0}:⟹x²+2x−143=0

\sf{:\implies x²+13x-11x-143=0}:⟹x²+13x−11x−143=0

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

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

\sf{:\implies x=-13}:⟹x=−13

or,

\boxed{\bf{\pink{⟹\:x=11}}}

⟹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