Question
If a3 = 117 + b3 and a = 3 + b,
then the value of a + b is:Solution
a3 – b3 = 117 and a – b = 3 ⇒ a3 – b3 = (a – b) (a2 + b2 +ab) ⇒ 117 = 3 (a2 + b2 +ab) ⇒ 39 = a2 + b2 +ab ⇒ a2 + b2 = 39 – ab we Know that (a-b)² = a2 +b² - 2ab                        = (a-b)² = 39 – ab – 2ab                        = (a-b)² = 39 – 3ab                 9   = 39 – 3ab = ab = 10 Now use (a+b)² = a2 + b2 + 2ab (a+b)² = 39 – ab + 2ab (a+b)² = 39 + ab = 39 + 10 (a+b)² = 49 = a + b = ±7 Â
((99.9 - 20.9)² + (99.9 + 20.9)² )/(99.9 x 99.9 + 20.9 x 20.9) = ?
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If p = 33 - q - r and pq + r(q + p) = 260, then find the value of (p² + q² + r²).
