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Statement 1: (A+B)² > 200.[email protected] wrote:Q: IS A^2 + B^2 > 100 ?
A: (A + B)^2 > 200
B: 2AB <100
MY ANSWER IS C. BUT OA IS A
Since the square of a value cannot be negative, (A-B)² ≥ 0.
Adding together (A+B)² > 200 and (A-B)² ≥ 0, we get:
(A+B)² + (A-B)² > 200+0.
(A² + 2AB + B²) + (A² - 2AB + B²) > 200.
2A² + 2B² > 200.
A² + B² > 100.
Sufficient.
Statement 2: 2AB < 100.
Thus, AB < 50.
If A=1 and B=1, then A²+B² < 100.
If A=2 and B=10, then A²+B² > 100.
Insufficient.
The correct answer is A.
