Aptitude · all questions

Algebra
practice.

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Q381

Open question

If 2x + 3y - 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx ?

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Q382

Open question

If x + y = 4, xy = 2, y + z = 5, yz = 3, z + x = 6 and zx = 4, then find the value of x³ + y³ + z³ - 3xyz.

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Q383

Open question

If x = 2 - p, then x³ + 6xp + p³ is equal to:

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Q384

Open question

Simplify the following expression:

\frac{( a ^{2} - 4 b ^{2} ) ^{3} + 64 ( b ^{2} - 4 c ^{2} ) ^{3} + ( 16 c ^{2} - a ^{2} ) ^{3}}{( a - 2 b ) ^{3} + ( 2 b - 4 c ) ^{3} + ( 4 c - a ) ^{3}}

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Q385

Open question

x is a negative number such that k + k^-1 = -2, then what is the value of

\frac{k ^{2} + 4 k - 2}{k ^{2} + k - 5} ?

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Q386

Open question

If a + b + c = 2,

\frac{1}{a} + \frac{1}{b} + \frac{1}{c}

= 0, ac =

\frac{4}{b}

and a³ + b³ + c³ = 28, find the value of a² + b² + c².

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Q387

Open question

If x =

2 - 2^{\frac{1}{3}} + 2^{\frac{2}{3}},

then find the value of x³ - 6x² + 18x.

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Q388

Open question

If a + b + c + d = 2, then the maximum value of (1 + a)(1 + b)(1 + c)(1 + d) is:

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Q389

Open question

If 3a = 4b = 6c and a + b + c =

2729

then

a^{2} + b^{2} + c^{2}

is equal to

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Q390

Open question

\frac{x ^{2} + 1}{x} = 4 \frac{1}{4},

then what is the value of

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

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Q391

Open question

If a² + b² + c² +

\frac{1}{a ^{2}} + \frac{1}{b ^{2}} + \frac{1}{c ^{2}} = 6,

then what is the value of a² + b² + c²?

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Q392

Open question

The factors of x² + 4y² + 4y - 4xy - 2x - 8 are:

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Q393

Open question

\frac{4}{3} (x^{2} + \frac{1}{x ^{2}}) = 110 \frac{2}{3},

find

\frac{1}{9} (x^{3} - \frac{1}{x ^{3}}),

where x > 0.

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Q394

Open question

If 27x³ - 64y³ = (Ax + By) (Cx² - Dy² + 12xy) then the value of 4A + B + 3C + 2D is:

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Q395

Open question

If a + 3b = 12 and ab = 9, then the value of (a - 3b) is:

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Q396

Open question

Determine the value of 'x', if

x = \frac{( 943 + 864 ) ^{2} - ( 943 - 864 ) ^{2}}{( 1886 \times 1728 )}

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Q397

Open question

The value of

\frac{48.3 \times [ ( 4.95 ) ^{2} + 4.95 \times 13.25 ]}{[ ( 12.55 ) ^{2} - ( 5.65 ) ^{2} ] \times 19.8} = ?

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Q398

Open question

a^{2} + \frac{2}{a ^{2}} = 16,

then find the value of

\frac{72 a ^{2}}{a ^{4} + 2 + 8 a ^{2}} .

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Q399

Open question

If a² + b² = 4b + 6a - 13, then what is the value of a + b?

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Q400

Open question

If a + b + c = 0, then the value of

\frac{a ^{2}}{b c} + \frac{b ^{2}}{c a} + \frac{c ^{2}}{ab}

is:

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Algebrapractice.

Algebra
practice.