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A14) a + b + c = 9 and ab + bc + ac = 23
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
9² = a² + b² + c² + 2(23)
81 = a² + b² + c² + 46
a² + b² + c² = 81 - 46 = 35.
A15) √125 - 4√6 + √294 - 2√(1/6)
5√5 - 4√6 + 7√6 - 2/√6
5√5 + 3√6 - 2/√6 is the answer
A16) x² - 1/x² = 18
x² - 1/x² = (x - 1/x)² + 2
So,
(x - 1/x)² + 2 = 18
(x - 1/x)² = 16
x - 1/x = 4
x³ - 1/x³ = (x - 1/x)³ + 3(x - 1/x)
= 4³ + 3(4)
= 64 + 12
= 76
Hope this helps you.
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
9² = a² + b² + c² + 2(23)
81 = a² + b² + c² + 46
a² + b² + c² = 81 - 46 = 35.
A15) √125 - 4√6 + √294 - 2√(1/6)
5√5 - 4√6 + 7√6 - 2/√6
5√5 + 3√6 - 2/√6 is the answer
A16) x² - 1/x² = 18
x² - 1/x² = (x - 1/x)² + 2
So,
(x - 1/x)² + 2 = 18
(x - 1/x)² = 16
x - 1/x = 4
x³ - 1/x³ = (x - 1/x)³ + 3(x - 1/x)
= 4³ + 3(4)
= 64 + 12
= 76
Hope this helps you.
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