Question

find the real number X and Y gives that x-y=3/2 and x power 4+ y power four= 2657/16​

Answer 1

Answer:

The real number of X and Y is 161 and 6 respectively.

Step-by-step explanation:

Given:

Find the real number X and Y gives that x-y=\frac{3}{2} and x power 4+ y power four= \frac{2657}{16}

Solution:

x – y = $\frac{3}{2}$, adding power to the 4 on both sides,  

$(x - y)^4  = (\frac{3}{2})^4$

$X^4 + y^4 - 4x^3y + 6x^2y^2 - 4xy^3 = \frac{81}{16}$

$\frac{2657}{16} - 4x^3y + 2x y^2 (x - y) = \frac{81}{16}$

$\frac{2657}{16} - 4x^3y + 2x y^2 \times \frac{3}{2} = \frac{81}{16}$

$\frac{2657}{16} + 3xy^2 - 4x^3y = \frac{81}{16}$

161 = 4xy (x  – y)

161 = 4xy ($\frac{3}{2}$)

161 = 6xy

$\frac{161}{6}$ = xy

Result:

The real number of X and Y is 161 and 6 respectively.

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