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Class 11 Math Algebra Logarithm and Antilogarithm

Solve the following system of equations.
\displaystyle\, \frac{x}{y^2} + \frac{y}{x^2} = \frac{9}{8}, \log_2\, x + \log_\sqrt{2}\, \sqrt{y} = 3

Solution:

\frac{x}{y ^{2}} + \frac{y}{x ^{2}} = \frac{9}{8}

x^{3} + y^{3} = \frac{9}{8} (x y)^{2} \to 1

lo g_{2} x + lo g_{2} y = 3

lo g_{2} x + lo g_{2} y = 3

lo g_{2} x = 3

(x y) = 2^{3} = 8

(x y) = 8 \to 2

From

1

and

2

x^{3} + (\frac{8}{x})^{3} = \frac{9}{8} (8)^{2}

x^{6} + (8)^{3} = (72) x^{3}

x^{6} - 72 x^{3} + (8)^{3} = 0

x^{3} = \frac{7 2 \pm ( 7 2 ) ^{2} - 4 ( 8 ) ^{3}}{2} = \frac{7 2 \pm ( 5 6 ) ^{2}}{2}

x^{3} = \frac{7 2 \pm 5 6}{2} = 64, 8

x = 2, 4

From

2

:

x y = 8

y = \frac{8}{x} y = \frac{8}{2} = 4, y = \frac{8}{4} = 2

(x, y) : (2, 4), (4, 2)

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Similar topics

determinants

matrices

binomial theorem

complex numbers and quadratic equations

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Home
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Copyright FILO EDTECH PVT. LTD. 2021