Question
If (6m – 5n) 2 = 7 and 30mn = 60, then
find the value of (6m + 5n) 2 + 16mn.Solution
(6m – 5n) 2 = 7
Using, (a – b) 2 = (a + b) 2 – 4ab
(6m + 5n) 2 – 4 × (6m) × (5n) = 7
(6m + 5n) 2 – 4 × (30mn) = 7
(6m + 5n) 2 – 4 × 60 = 7
(6m + 5n) 2 – 240 = 7
(6m + 5n) 2 = 247
16mn = 16 × (60/30) = 32
So, (6m + 5n) 2 + 16mn = 247 + 32 = 279
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