Mathematics
If x + y = 8 and x - y = 2, find the value of 2x2 + 2y2.
Expansions
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Answer
We know that,
(x + y)2 = x2 + y2 + 2xy …..(i)
(x - y)2 = x2 + y2 - 2xy ….(ii)
Adding eqn. (i) and (ii) we get,
(x + y)2 + (x - y)2 = x2 + x2 + y2 + y2 + 2xy - 2xy
= 2x2 + 2y2.
∴ 2x2 + 2y2 = (x + y)2 + (x - y)2.
Substituting values we get,
⇒ 2x2 + 2y2 = (8)2 + (2)2
⇒ 2x2 + 2y2 = 64 + 4 = 68.
Hence, 2x2 + 2y2 = 68.
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