If \(x - y = 8\) and \(xy = 5\), what is the value of \(x^{3} - y^{3}+ 8(x + y)^{2}\) .
1304
Use \(x^{3} - y^{3} = (x - y)^{3} + 3xy(x - y)\) and \((x + y)^{2} = (x - y)^{2} + 4xy\).
\(x^{3} - y^{3} = 8^{3} + 3 \times 5 \times 8 = 512 + 120 = 632\)
\((x + y)^{2} = 8^{2} + 4 \times 5 = 64 + 20 = 84\)
Value = 632 + 8 × 84 = 632 + 672 = 1304
Check: \(x^{2} + y^{2} = 64 + 2 \times 5 = 74\), and \((x - y)(x^{2} + xy + y^{2}) = 8 \times 79 = 632\), confirming the cube part.
Hence, 1304.
Similar Questions
If \(p + q = 3\) and \(p - q = 1\), find \(2p^2 + 2q^2 - 4pq\).
If a+b = 3 and a-b = 1, find the value of \(a^4 - b^4\).
\(\dfrac{(3.57)^2 + (4.54)^2 + 32.4156}{(4.54)^2 - (3.57)^2} = ?\)
Simplify: \(\dfrac{\left(a^{2}-b^{2}\right)^{3}+\left(b^{2}-c^{2}\right)^{3}+\left(c^{2}-a^{2}\right)^{3}}{(a-b)^{3}+(b-c)^{3}+(c-a)^{3}}\)
Simplify the following expression:
\(\dfrac{(25)^4+1250+1-(25)^2}{(25)^2+26}\)
If \(x - y = 7\) and \(xy = 60\), then what is the value of \(x^2 + y^2\)?
If \(x + y = 12\) and \(x - y = 4\), find \(\dfrac{x^{3}+y^{3}}{x+y}\).
Find the value of:
\((\sqrt{5} + 2)^2 - (\sqrt{5} - 2)^2\)
If \(x + y = 11\) and \(x - y = 5\), find \(x^4 - y^4\).
If \(x + y = 7\) and \(xy = 12\), calculate the value of \(x^{2} + y^{2}\).
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=
