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If a2 + b2 = 80 and ab = 32, then calculate the value of \(\frac{{a - b}}{{a + b}}\).
- A0.337
- B0.339
- C0.333
- D0.335
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CCommunity
a2 + b2 = 80 and ab = 32
(a + b)2 = a2 + b2 + 2ab = 80 + 2 × 32 = 80 + 64 = 144
⇒ a + b = 12
(a – b)2 = a2 + b2 – 2ab = 80 – 2 × 32 = 80 – 64 = 16
⇒ a – b = 4
$(\frac{{a - b}}{{a + b}} = \frac{4}{{12}} = \frac{1}{3} = 0.333)$
(a + b)2 = a2 + b2 + 2ab = 80 + 2 × 32 = 80 + 64 = 144
⇒ a + b = 12
(a – b)2 = a2 + b2 – 2ab = 80 – 2 × 32 = 80 – 64 = 16
⇒ a – b = 4
$(\frac{{a - b}}{{a + b}} = \frac{4}{{12}} = \frac{1}{3} = 0.333)$