If a + b = 5 and a² + b² = 17, find (a³ + b³)/ab.
65/4
Since \((a+b)^2 = a^2+b^2+2ab\), we get \(ab = \frac{(a+b)^2-(a^2+b^2)}{2} = \frac{25-17}{2} = 4\).
Using \(a^3+b^3 = (a+b)(a^2+b^2-ab)\), we get \(a^3+b^3 = 5(17-4) = 5 \times 13 = 65\).
Therefore, \(\frac{a^3+b^3}{ab} = \frac{65}{4}\).
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Important Questions from Identities
If x 2 + 4y 2 = 40, xy = 6 and x > 2y then the value of x - 2y is:
- \(\dfrac{(5.17-2.19)^2-(5.17+2.19)^2}{11.3223}\)
If a(a + b + c) 2= 1792; b(a + b + c) 2= 1536; c(a + b + c) 2= 768 then what will be the value of a?
If a + b + c = 5, a 2+ b 2+ c 2= 27, a 3 + b 3 + c 3 = 125, then the value of \(\frac{abc}{5}\) is:
(999) 2- 2 2=
