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Algebra
practice.

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Q501

Open question

If x + y + z = 19, x² + y² + z² = 133, and xz = y², x > z > 0, what is the value of (x - z)?

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Q502

Open question

c - d = \frac{c + d}{5} = \frac{c d}{3}

and c, d ≠ 0 then what is the value of cd?

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Q503

Open question

If x² - 4x + 1 = 0, then what is the value of x⁹ + x⁷ - 194x⁵ - 194x³?

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Q504

Open question

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

then the value of

A - \frac{1}{A}

is:

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Q505

Open question

If x + y = 3, then what is the value of x³ + y³ + 9xy?

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Q506

Open question

x^{2} + \frac{1}{x ^{2}} = 7,

then the value of

x^{3} + \frac{1}{x ^{3}}

where x > 0 is equal to:

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Q507

Open question

If x = 5 + 2√6, then what is the value of

x + \frac{1}{x} ?

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Q508

Open question

If x⁴ + x^-4 = 194, x > 0, then what is the value of

x + \frac{1}{x} + 2 ?

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Q509

Open question

If (a + 4)³ = a³ + 12a² + ka + 64, then what is the value of k?

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Q510

Open question

If (135√5x² - 2√2y³) ÷ (3√5x - √2y) = Ax² + By² +

10

Cxy, then the value of (A + B - 9C) is:

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Q511

Open question

If a - b = 4 and a³ - b³ = 88, then find the value of a² - b².

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Q512

Open question

If x³ + y³ + z³ = 3(1 + xyz), P = y + z - x, Q = z + x - y and R = x + y - z, then what is the value of P³ + Q³ + R³ - 3PQR?

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Q513

Open question

If ab(a + b) = 1, then what is the value of

\frac{1}{a ^{3} b ^{3}} - a^{3} - b^{3} ?

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Q514

Open question

ab(a - b) + bc(b - c) + ca(c - a) is equal to:

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Q515

Open question

\frac{a + b}{c} = \frac{6}{5}

and

\frac{b + c}{a} = \frac{9}{2},

then what is the value of

\frac{a + c}{b} ?

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Q516

Open question

Simplify

\frac{x ^{2} + 2 x + y ^{2}}{x ^{3} - 5 x ^{2}} if x + \frac{y ^{2}}{x} = 5.

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Q517

Open question

If a - b = 18 and a³ - b³ = 324, then find the value of ab.

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Q518

Open question

If x - y = 3, then what is the value of x³ - y³ - 9xy?

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Q519

Open question

What is the simplified value of

(x + \frac{1}{x}) (x^{2} + \frac{1}{x ^{2}}) (x^{4} + \frac{1}{x ^{4}}) (x^{8} + \frac{1}{x ^{8}}) (x^{16} + \frac{1}{x ^{16}}) is:

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Q520

Open question

A = \frac{( 0.1 ) ^{3} + ( 0.2 ) ^{3} + ( 0.3 ) ^{3} + 3 ( 0.005 + 0.016 + 0.027 ) + 0.036}{( 0.1 ) ^{2} + ( 0.2 ) ^{2} + ( 0.3 ) ^{2} + 0.04 + 0.06 + 0.12}

then the value of 60A is:

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Algebrapractice.

Algebra
practice.