Question

\(\sqrt{25-x^2}-\sqrt{9-x^2}=2\)

Answer 1

ĐKXĐ: -3 ≤ x ≤ 3

Ta có √25 − x^2 − √9 − x^2 = 2

<=> √25 − x^2 = 2 + √9 − x^2

<=> (√25 − x^2)^2 = (2 + √9 − x^2)^2

<=> 25 - x^2 = 4 + 4.√9 − x^2 + 9 - x^2

<=> 12 - x^2 = 4.√9 − x^2 - x^2

<=> 12 = 4.√9 − x^2

<=> √9 − x^2 = 3

<=> 9 − x^2 = 9 <=> x^2 = 0 <=> x = 0

Vậy x = 0