Question

The sum of the squares of the two consecutive even numbers is 340 . Find the numbers.

Answer 1

✬ Numbers = 12 & 14 ✬

Step-by-step explanation:

Given:

• Sum of squares of two consecutive even numbers is 340.

To Find:

• What are the two numbers ?

Solution: Let the consecutive even numbers be x & x + 2.

A/q

• Square of these number is 340.

$\implies{\rm }$ (x)² + (x + 2)² = 340

$\implies{\rm }$ x² + x² + 2² + 2•x•2 = 340

$\implies{\rm }$ 2x² + 4x = 340 – 4

$\implies{\rm }$ 2x (x + 2) = 336

$\implies{\rm }$ x (x + 2) = 336/2

$\implies{\rm }$ x² + 2x = 168

$\implies{\rm }$ x² + 2x – 168 = 0

Now, By using middle term splitting method.

➨ x² + 2x – 168

➨ x² + 14x – 12x – 168

➨ x (x + 14) – 12 (x + 14)

➨ (x + 14) (x – 12)

➨ (x + 14) = 0 or, (x – 12) = 0

➨ x = –14 or x = 12

Reject the negative value of x and take x = 12

Hence, Required number are

➬ x = 12 and (x + 2) = 12+2 = 14

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★ Verification ★

• 12² + 14² = 340

• 144 + 196 = 340

• 340 = 340

[ Verified ]

Answer 2

GIVEN:

• The sum of the squares of the two consecutive even numbers is 340

TO FIND:

• Find the numbers ?

SOLUTION:

Let the two consecutive numbers be 'x' and 'x+2'

It is given that, the sum of the squares of the two consecutive even numbers is 340

According to question:-

$\rm{\dashrightarrow (x)^2 + (x+2)^2 = 340}$

Using Identity

• (a+b)² = a² + 2ab + b²

$\rm{\dashrightarrow x^2 + x^2 + 4x + 4= 340}$

$\rm{\dashrightarrow 2x^2 + 4x = 340-4 }$

$\rm{\dashrightarrow 2x^2 + 4x - 336 = 0}$

Taking common 2 from both sides

$\rm{\dashrightarrow x^2 + 2x - 168 = 0 }$

$\rm{\dashrightarrow x^2 +(14-12)x-168 = 0 }$

$\rm{\dashrightarrow x^2 +14x -12x -168=0}$

$\rm{\dashrightarrow x(x+14) -12(x+14) = 0}$

$\rm{\dashrightarrow (x + 14)(x - 12) = 0 }$

$\rm{\dashrightarrow x = -14 (Neglected) }$

$\bf{\dashrightarrow x = 12 }$

• First Number = x = 12
• Another number = x+2 = 12+2 = 14

❝ Hence, the two numbers are 12 and 14. ❞

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