Question

QUADRATIC EQUATIONS
Find two consecutive even integers whose squares
have the sum 340. give solution​

Answer 1

$\huge\star{\underline{\mathtt{\red{Q}\pink{U}\green{E}\blue{ST}\purple{I}\orange{ON}}}}⋆$→

Find two consecutive even integers whose squares have the sum 340.

$\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}⋆$

Let two consecutive positive even integers be 2x, 2x + 2

∴ (2x)2 + (2x + 2)2 = 340

⇒ 4x2 + 4x2 + 4 + 8x = 340

⇒ 8x2 + 8x – 336 = 0

⇒ x2 + x – 42 = 0

⇒ x2 + 7x – 6x – 42 = 0

⇒ x(x + 7) – 6(x + 7) = 0

⇒ (x + 7)(x – 6) = 0

⇒ x + 7 = 0 or x – 6 = 0

⇒ x = - 7 or x = 6

Negative integer is not required, therefore, x = 6.

Hence, integers are 6 × 2, (6 × 2) + 2.

i.e., 12 and 14.

Hope it helps you :]