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If a + b = 13 and a2 + b2 = 5. Find ab.
70
75
80
82
a + b = 13
∴ (a + b)2 = 169
∴ a2 + 2ab + b2 = 169 … using (a + b)2 = a2 + 2ab + b2
∴ 5 + 2ab = 169 … since a2 + b2 = 5
∴ ab = 82
If a = 2x and b = 3, then (a − b) 2 =?
2x2 - 12x + 9
4x2 - 12 + 9
4x2 - 12x + 9
4x2 - 12x + 3
Since (a − b)2 = a2 − 2ab + b2
(a − b)2 =(2x − 3)2 = 4x2 - 2 × 2x × 3 + 9 = 4x2 - 12x + 9
Simplify: (x2 − y2)2 + 2 (x2 − y2)(x2 + y2) + (x2 + y2)2
4y4
4x4
2x4
2y4
Let (x2 − y2) = a and (x2 + y2) = b
∴ (x2 − y2)2 + 2 (x2 − y2)(x2 + y2) + (x2 + y2)2 = a2 + 2ab + b2
Since (a + b)2 = a2 + 2ab + b2
∴ (x2 − y2 + x2 + y2)2 = (2x2)2 = 4x4
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