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Algebraic Identities

If x + y = ...

Question

If $x + y = 5, x^{3} + y^{3} = 35$ , then $x - y$ is equal to

A

0

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B

\pm 1

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C

5

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D

30

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Solution

The correct option is C $\pm 1$
$(x + y)^{3} = x^{3} + y^{3} + 3 x y (x + y)$
or $5^{3} = 35 + 3 x y (5)$
or $125 - 35 = 15 x y$
or $x y = \frac{90}{15} = 6$
Now, $(x - y)^{2} = (x + y)^{2} - 4 x y$
$= 5^{2} - 4 \times 6$
$= 25 - 24 = 1$
$∴ x - y = \sqrt{1} = \pm 1$

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Similar questions

x + y - 1 = 0

x^{3} + y^{3} - 1

\frac{x}{y} + \frac{y}{x}

\neq

x^{3} + y^{3}

+3xy(x + y) is equal to:

x + y = 5

x^{2} + y^{2} = 111

, then value of

x^{3} + y^{3}

\frac{x}{y} + \frac{y}{x} = - 1, (x, y \neq 0)

, then value of

x^{3} - y^{3}

y + \frac{y^{3}}{3} + \frac{y^{5}}{5} + . . . \infty = 2 [x + \frac{x^{3}}{3} + \frac{x^{5}}{5} + . . . \infty]

, then the relation between

x

y

x^{2} y = a x - y

2 a + 1

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