If [√(a2 + b2 + ab)] + [√(a2 + b2 – ab)] = 1, then what is the value of (1 – a2 )(1 – b2 )?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 3/4
[√(a2 + b2 + ab)] + [√(a2 + b2 – ab)] = 1
[√(a2 + b2 + ab)] = 1 - [√(a2 + b2 – ab)]
squaring both sides
a2 + b2 + ab = 1 + a2 + b2 – ab - 2√(a2 + b2 – ab)
2ab - 1 = 2√(a2 + b2 – ab)
Again squaring both sides
4a2b2 +1 - 4ab = 4a2 + 4b2 - 4ab
4(a2b2 - a2 - b2 + 1) = 3
(a2 - 1)(b2 - 1) = 3/4
therefore, (1 – a2 )(1 – b2 ) = 3/4