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If a + b is equals to 12 and a b is equal to 27 find the value of a cube plus b cube |
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Answer» Answer: a³ + b³ = 756 Step-by-step explanation: a + b = 12 ------(1) ab = 27 ------(2) from eq. 1 a + b = 12 a = 12 - b PUT a in eq. 2 ab = 27 (12 - b)b = 27 12B - b² = 27 b² - 12b + 27 = 0 b² - 9b - 3b + 27 = 0 b(b - 9)*-3(b - 9) = 0 (b - 9)(b - 3) = 0 b = 9 or b = 3put b in eq. 1 (if, b = 3) a + b = 12 a + 3 = 12 a = 12 - 3 a = 9 (if, b = 9) a + 9 = 12 a = 12 - 9 a = 3 now, a³ + b³ (if a=3 and b=9) = (3)³ + (9)³ = 27 + 729 = 756 or, if a = 9 and b = 3 then, a³ + b³ = (9)³ + (3)³ = 729 + 27 = 756 so , a³ + b³ = 756
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