Question

the sum of the square is two consecutive even is 340. find the number . step by step​

Answer 1

Answer:

2

Step-by-step explanation:

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Answer 2

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

Verification

• 12² + 14² = 340

• 144 + 196 = 340

• 340 = 340

[ Verified ]