Question

Two consecutive odd positive integers , sum of whose squares is 290. Quadratic equation for this statement is-

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer

Given,

• Sum of squares of two consecutive positive odd integers = 290

To find ,

The consecutive positive odd integers

Solution ,

Let one positive odd integer be 'x' then its successive odd integer will be 'x+2'

According to the condition:

⇒ x² + ( x +2 )² = 290

⇒ x² + x² + 4 + 4x = 290

(( a + b)² = a² + b² + 2ab )

⇒ 2x² + 4x + 4 - 290 = 0

⇒ 2x² + 4x - 286 = 0

Dividing the equation by '2'

⇒ x² + 2x - 143 = 0

Here we got a quadratic equation, Let us solve it by splitting the middle term method

⇒ x² + 13x - 11x - 143 = 0

⇒ x(x + 13) -11(x + 13) = 0

⇒ (x - 11)(x + 13) = 0

i.e

• x = 11
• x = -13

We were already given the 'x' is a positive odd integer.

Hence x = 11

So,

⇒ x + 2 = 11 + 2

⇒ x + 2 = 13

Hence the two consecutive positive odd integers are 11 & 13