Question

The sum of the square of two consecutive odd natural numbers is 299. find the number.
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Answer 1

• CORRECT QUESTION:-

The sum of the square of two consecutive odd natural numbers is 290.

• To Find:-

Find the numbers.

• SOLUTION:-

Let the two odd natural consecutive numbers be x, x + 2.

It is said the sum of their squares is 290.

According to the question,

$\large\Longrightarrow{\sf{{(x)}^{2}+{(x+2)}^{2}=290}}$

$\large\Longrightarrow{\sf{({x)}^{2}+({x}^{2}+4x+4)=290}}$

$\large\Longrightarrow{\sf{{2x}^{2}+4x+4=290}}$

$\large\Longrightarrow{\sf{{2x}^{2}+4x+4-290=0}}$

$\large\Longrightarrow{\sf{{2x}^{2}+4x-186=0}}$

Dividing both sides by 2,

$\large\Longrightarrow{\sf{{x}^{2}+2x-143=0}}$

$\large\Longrightarrow{\sf{x(x+13)-11(x+13)=0}}$

$\large\Longrightarrow{\sf{(x+13)(x-11)=0}}$

$\large\therefore{\sf{x+13=0}}$

$\large\therefore{\sf{x-11=0}}$

$\large\therefore{\sf{x=-13}}$

We cannot take negative values.

So,

$\large\therefore{\sf{x=11}}$

x = 11

x + 2 = 11 + 2 = 13

$\large\red\therefore\boxed{\sf{\red{Two \:consecutive\: odd\: natural \:numbers\: are \:11\: and\: 13.}}}$

Answer 2

CORRECT QUESTION:-

The sum of the square of two consecutive odd natural numbers is 290.

To Find:-

Find the numbers.

SOLUTION:-

Let the two odd natural consecutive numbers be x, x + 2.

It is said the sum of their squares is 290.

According to the question,

$\large\Longrightarrow{\sf{{(x)}^{2}+{(x+2)}^{2}=290}}$

$\large\Longrightarrow{\sf{({x)}^{2}+({x}^{2}+4x+4)=290}}$

$\large\Longrightarrow{\sf{{2x}^{2}+4x+4=290}}$

$\large\Longrightarrow{\sf{{2x}^{2}+4x+4-290=0}}$

$\large\Longrightarrow{\sf{{2x}^{2}+4x-186=0}}$

Dividing both sides by 2,

$\large\Longrightarrow{\sf{{x}^{2}+2x-143=0}}$

$\large\Longrightarrow{\sf{x(x+13)-11(x+13)=0}}$

$\large\Longrightarrow{\sf{(x+13)(x-11)=0}}$

$\large\therefore{\sf{x+13=0}}$

$\large\therefore{\sf{x-11=0}}$

$\large\therefore{\sf{x=-13}}$

We cannot take negative values.

So,

$\large\therefore{\sf{x=11}}$

x = 11

x + 2 = 11 + 2 = 13

$\small\red\therefore\boxed{\sf{\red{Two \:consecutive\: odd\: natural \:numbers\: are \:11\: and\: 13.}}}$