Aptitude · all questions

Algebra
practice.

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Q461

If x + y + z = 10, x³ + y³ + z³ = 75 and xyz = 15, then find the value of x² + y² + z² - xy - yz - zx.

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Q462

If x + y + z = 17, xyz = 171 and xy + yz + zx = 111, then the value of

\root 3 \of (x^{3} + y^{3} + z^{3} + x y z)

is:

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Q463

If x + y = 14 and x³ + y³ = 1064, then the value of (x - y)² is:

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Q464

If

p + \frac{1}{p} = 112,

find the value of

(p - 112)^{15} + \frac{1}{p ^{15}} = ?

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Q465

If x = 1 + √2 + √3, then find the value of x² - 2x + 4.

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Q466

If a² + b² + c² + 96 = 8(a + b - 2c), then

ab - b c - c a

is equal to

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Q467

If

x + \frac{1}{x} = \frac{3 + 1}{2},

then what is the value of

x^{4} + \frac{1}{x ^{4}} ?

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Q468

If x = 2 + √3, then find the value of x⁴ - 8x³ + 16x².

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Q469

The value of

\frac{7 + 8 \times 8 \div 8 of 8 + 8 \div 8 \times 4 of 4}{4 \div 4 of 4 + 4 \times 4 \div 4 - 4 \div 4 of 2} is:

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Q470

If

3 \frac{1 - a}{a} + 9 = 19 - 3 \frac{a}{1 - a},

then what is the value of a?

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Q471

If (5x + 1)³ + (x - 3)³ + 8(3x - 4)³ = 6(5x + 1)(x - 3)(3x - 4), then x is equal to:

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Q472

The value of

\frac{1}{4} + \frac{[ ( 20.35 ) ^{2} - ( 8.35 ) ^{2} ] \times 0.0175}{( 1.05 ) ^{2} + ( 1.05 ) ( 27.65 )} is:

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Q473

If a³ + b³ = 218 and a + b = 2, then the value of

1 - ab

is:

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Q474

If [8(x + y)³ - 27(x - y)³] ÷ (5y - x) = Ax² + Bxy + Cy², then the value of (A + B + C) is:

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Q475

If x³ - 4x² + 19 = 6(x - 1) then what is the value of

[x^{2} + \frac{1}{x - 4}] ?

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Q476

If (5√5x³ - 3√3y³) ÷ (√5x - √3y) = (Ax² + By² + Cxy), then what is the value of (3A - B -

15

C)?

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Q477

If

x + \frac{1}{x} = 32,

then what is the value of

x^{5} + \frac{1}{x ^{5}} ?

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Q478

If x³ + 27y³ + 64z³ = 36xyz, then the relationship between x, y and z is:

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Q479

If (x + y + z) = 0, then what is the value of

\frac{3 y ^{2} + x ^{2} + z ^{2}}{2 y ^{2} - x z} ?

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Q480

If

x + \frac{1}{x} = - 14,

and x < -1 what will be the value of

x^{2} - \frac{1}{x ^{2}} = ?

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