If a³ + b³ + c³ - 3abc = 252 and a + b + c = 6. Find the value of ab + bc + ca.

If x + y + z = 4, xy + yz + zx = 1 and x³ + y³ + z³ = 34, then what is the value of 6xyz?

If ab + bc + ca = 119 , a² + b² + c² = 162 and a, b & c are positive values then what is the value of a²(b + c) + b²(c + a) + c²(a + b) +3abc ?

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

\(\frac{a^2-(b-c)^2}{(a+c)^2-b^2} + \frac{b^2-(a-c)^2}{(a+b)^2-c^2} +  \frac{c^2-(a-b)^2}{(b+c)^2-a^2} = ?\)

If p + q + r = pqr = \(\frac{1}{p} + \frac{1}{q} +\frac{1}{r} \) = 1 then find p³ + q³ + r³.

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

If a = 2.3 and b = 0.7, find the value of 9a² + 12ab + 4b². 

Simplify: (2a - 3b - c)² - (a + 2b + c)²

If ab + bc + ca = 0, then find the value of \( {{1} \over a^2-bc}+ {{1} \over b^2-ca}+ {{1} \over c^2-ab}\)

If a² + b² + 49 c² + 18 = 2 (b - 28c - a) then the value of (a + b - 7c) is:

What is the value of (a + b + 2c) (a² + b² + 4c² - ab - 2abc - 2ca)?

If 8a³ + b³ + 27c³ = 18abc, then the relation among a, b and c is:

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 xy = 6 and \(x^2y + xy^2 + x + y = 63,\) then the value of x² + y² is :

If 2a² + 2b² + 2c² + 4ab + 4bc + 4ca + 3a + 3b + 3c = 0 and a + b + c ≠ -3/2, a ≠ b ≠ c ≠ 0, then what is the value of (a + b + c + abc)/(a³ + b³ + c³)?

 If a³ + b³ + c³ - 3abc = 126, a + b + c = 6 , then the value of (ab + bc + ca) is:

If 16x² + y² = \(65\over36\) and xy = \(1\over18\), x, y < 0, then what is the value of (64x³ + y³)?

If l + m  + n = 0, then what will be the value of \((\frac{l^2}{mn}+\frac{m^2}{nl}+\frac{n^2}{lm})\) ?
 

If 3^a = 27^b = 81^c and abc = 144, then the value of \(12\left(\frac{1}{a}+\frac{1}{2b}+\frac{1}{5c}\right)\) is

If ax + by = 1 and bx + ay = \(2ab\over{a^2+b^2}\) then the value of x (in terms of a and b) is:
 

If a² + b² = 169, ab = 10, and a > b, find \(a-b\over a+b\).

If (a – b) = 9, and (a³ – b³) = 4401, find the value of ab.

Which of the following statements is correct?

I. If x = 12, y = – 2 and z = –10, then x³ + y³ + z³ = 360

II. If x + y = 48 and 4xy = 128, then 4x² + 4y² = 4480

If  x + y + z = 6, xyz = -10 and  x² + y² + z² = 30 , then what is the value of  x³ + y³ + z³ = ?

If x + y + z = 10 and x² + y² + z²  =80 then what is the value of 4xy + 4yz + 4zx?

If (3x + 4y)(5x - 6y) = ax² + 2hxy + by² then what is the value of (4a - h + 2b)?

 If a² + 2(b - 1) (c - 1) = 73, b² + 2(c - 1)(a - 1) = 75.5, c² + 2(a - 1) (b - 1) = 78.5 then find a+b+c  where  a, b, c are positive numbers?

If a - b = 10 and ab = 4, then the value of a³ - b³ + 4(a + b)² is:

If x + y = 7 and xy = 19, then calculate the value of x² + y².

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

If 2a + 3b = 14 and 2a - 3b = 10, then find the value of 'ab'.

If x + 3y = 6, what is the value of x³ + 27y³ + 54xy?

If a + b + c = 16, ab + bc + ac = 81, what is the value of a² + b² + c²?

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

If (x + y) = 17, xy = 9, then what is the value of x³ + y³?

If (a – b) = 9, and (a³ – b³) = 4401, find the value of ab.

If x² – xy + y² = 13 and x⁴ + x²y² + y⁴ = 312, then the value of x² + y² is:

If a³ + b³ + c³ - 3abc = 250 and a + b + c = 10, then what is the value of ab + bc + ca?

If a + b + c = 6 & ab + bc + ca = 13, then find bc(b + c) + ca(c + a) + ab(a + b) + 3abc?

If x + y = 10 and xy = 12, find the value of x² - xy + y² .

If (a - 18)² + (b - 12)² + (c - 6)² = 0, then find the value of (a + b + c)^1/2.

If A +  B = - 5 and AB = 6, then find the value of A³ + B³

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

If \(x^2+y^2+z^2=xy+yz+zx\) and x = 1, then find the value of \(\frac{10x^4+5y^4+7z^4}{13x^2y^2+6y^2z^2+3z^2x^2}\)

If a + b + c = 16, ab + bc + ac = 81, what is the value of a² + b² + c²?

If 2a + 3b = 14 and 2a - 3b = 10, then find the value of 'ab'.

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

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

If (a - b) = 5 and ab = 150, then what is the value of (a³ - b³)?