Question

Find two consecutive positive even numbers,the sum of whose square is 452

Answer 1

Answer:

let the two consecutive even no be x and x+2

Step-by-step explanation:

(x)2+(x+2)2=452

x2 + x2 + 4x + 4= 452

2x2 + 4x + 4=452

2x2 + 4x - 448=0

2x2+ 32x - 28x - 448= 0

2x(x+32) -28(x+32)=0

(2x-28)(x+32)=0

either(2x-28)=0 or (x+32) = 0

= x = 28/2= 14

or x= -32 (neglecting it as no cannot be negative)

x= 14 and x+2= 14+2=16

hence the no are 14 and 16

hope it helps you

please mark as branliest answer

Answer 2

✬ 1st even number = 14 ✬

✬ 2nd even number = 16 ✬

Step-by-step explanation:

Given:

• Sum of squares of two consecutive positive even integers is 452.

To Find:

• What are two consecutive positive even integers ?

Solution: Let the first consecutive even integer be x therefore second will be (x + 2).

A/q

➨ Sum of squares is 452 i.e

➨ 452 = (x)² + (x + 2)²

$\implies{\rm }$ 452 = x² + (x² + 2² + 2•x•2)

$\implies{\rm }$ 452 = x² + x² + 4 + 4x

$\implies{\rm }$ 452 – 4 = 2x² + 4x

$\implies{\rm }$ 448 = 2x² + 4x

$\implies{\rm }$ 0 = 2x² + 4x – 448

$\implies{\rm }$ 0 = 2(x² + 2x – 224)

$\implies{\rm }$ 0 = x² + 2x – 224

Now, By using middle term splitting method

➮ x² + 2x – 224

➮ x² + 16x – 14x – 224

➮ x(x + 16) – 14 (x + 16)

➮ (x + 16) (x – 14)

➮ (x + 16) = 0 or (x – 14) = 0

➮ x = – 16 or x = 14

Since, x is an positive even integers so we will take the positive value of x. { Negative ignored }

Hence,

➱ First positive integer is x = 14

➱ Second positive integers is (x + 2)

=> (14 + 2) = 16

_____________________

★ Verification ★

→ 14² + 16² = 452

→ 196 + 256 = 452

→ 452 = 452

$\large\boxed{\texttt{Verified}}$