If x³ = 270 + y³ and x = (6 + y), then what is the value of (x + y)? (given that x > 0 and y > 0)

Simplify the given expression.

(a - 2b)(b - 3a) + (a + b)(a - 3b) - (b - 3a)(4a - 5b)

If (a + b + c) = 12, and (a² + b²+ c²) = 50, find the value of (a³ + b³ + c³ - 3abc).

If x + y + z = 4 and x² + y² + z² = 12, then find xy + yz + xz.

If (a + b + c) = 12, and (ab + bc + ca) = 47, find the value of (a³ + b³ + c³ - 3 abc).

If a + b + c =7, ab + bc + ca = 11 and abc = -1, then a³ + b³+ c³ is equal to:

If (a + b + c) = 20, a² + b² + c² = 152, find the value of a³ + b³ + c³ - 3abc.

If x = y - z then find the value of \(x^3-y^3+z^3\).

45x - 23y = 113

23x - 45y = 91

Find the value of the expression (x³ - y³).

Find the value of a + b + c, if a, b, and c are the three factors of x³– 7x – 6.

If p = 9, q = -7 and r = -2 then the value of p³ + q³ + r³  is ?

If (x + y + z) = 3a then find the value of the expression (a – x)³ + (a – y)³ + (a – z)³.

If (x - y) = 6, (y - z) = 10 and (z - x) = 2, find the value of 2 × [(a³ + b³ + c³ - 3abc)/(a + b + c)].

If (a + b)³ = 216 and ab = 5 , then what is the value of a³ + b³?

The sum of two numbers x and y is 15 and product of x and y is -54. What is the value of x³ + y³?

If x² + y² + z² = xy + yz + xz, then find the value of (x + y + z)/3x.

If (a + b) = 17 and ab = 72, then find the value of a³ + b³.

If a² + b² = 17, find the value of (a + b)² + (a - b)².

3a² + b² + 4ab + bc + 2ac = 19

3a² + 2b² + c² + 4ab + 2bc + 2ac = 26

If a, b and c are three positive integers, then what is the value of 3a + 2b + c?

If x and y are two positive integers such that x² + 4x + 4 – y² = 23, then what is the value of 3x – 2y?

If (ab + bc + ca) = 18 and (a + b + c) = 15, find the value of (a² + b² + c²).

If a² + 4b² + c² + 4ab + 2ac + 4bc = 64 and a² + b² + 4c² + 2ab + 4ac + 4bc = 81. What is the value of (a + 3b)? (a, b, c > 0)

If x + y + z = 19, x² + y² + z² = 133 and xz = y², then the difference between z and x is:

If x = 3y + 4, then what is the value of (x³ - 27y³ - 36 xy)?

If a + b = 11 and ab = 35, then what is the value of (a⁴ + b⁴)?

If (a³ + b³ + c³ - 3abc) = 405, and (a + b + c) = 15, find the value of (a - b)² + (b - c)² + (c - a)².

If p + q = 12 and pq = 14, then find the value of p² - pq + q².

If 2x + 5y = 15 and xy = 6, then the value of 4x² + 25y² is ____________.

If 4x² + y² = 40 and xy = 6, then find the value of 2x + y.

If (a + b + c) = 20 and a² + b² + c² = 262 then, find the value of ab+ bc + ca

If (x + y + z) = 3a then find the value of the expression (a – x)³ + (a – y)³ + (a – z)³.

If a²+b² = 148 and ab = 54, then find the value of \(\frac{a+b}{a-b}\).

If √a = 3b, then \(a\over b^2\) is equal to:

If \(2a-b=3\) and \(8a^3-b^3=999 \), then the value of \(4a^2-b^2\).

If a + b + c = 15 and ab + bc + ca = 22, then find the value of a² + b² + c².

If x = 459, y = 460, z = 463, then what is the value of x³+ y³ + z³ - 3xyz?

If a + b + c = 13 and ab + bc + ca = 45, find a² + b² + c².

If x + y + z = 9, x² + y² + z² = 57 and xyz = -12, then the value of x³ + y³ + z³ is:

If 2x + 3y = 9, and xy = 3, then find the value of 8x³ + 27y³.

If X = 110, Y = 111, Z = 112, then find the value of x³ + Y³ + Z³ - 3xyz.

If (a - b) = 12 and ab = 325, then find the value of (a³ - b³).

If y² + 9x² = 12 and yx = 6 then, find the value of (y + 3x)³/\(4\sqrt3\).

If 25a² + b² = 60, ab = 4, where a, b > 0 then, find the value of \(\sqrt{125a^3+b^3}\).

\(\sqrt{x^2+y^2+z^2 }\) = 27, and xy + yz + zx = 116, then find the value of (x + y + z), where (x + y + z) < 0.

if a² + b² = \(\frac{1}{a^2}\)(529 - b⁴), and a - b = \(\frac{1}{a}\)(46 - b²) then find the value of a² + b².

If 0.027x³ + 0.064y³ = 145, and 0.3x + 0.4y = 29 then find the value of (0.3x + 0.4y)² - 0.36xy.

If x = y - z then find the value of \(x^3-y^3+z^3\).

If (a² + b² + c²) = 64 , (ab + bc + ca) = 256 and abc = 987 then, find the value of (a³ + b³ + c³).

If (x + y)³ + 27 (x - y)³ = (Ax - 2y) (Bx² + Cxy + 13 y²), then the value of A - B - C is:

If x³ + y³ = 88 and x + y = 4 then what would be the value of xy, where x and y are the real numbers?