1.

4/x -9/y= -1 and 15x/2 -5y=0. Solve for x and y

Answer»

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Step-by-step explanation:

Solution: We have, 3X8 = 2X12. So, we write the given equation in the following form:

[(x + 2)(x + 12)][(x + 3)(x + 8)] = 4x2

=> (x2 + 14x + 24)(x2 + 11x + 24) = 4x2

Dividing throughout by x2, we get

(x + 14 + 24/x)(x + 11 + 24/x) = 4

=> (y + 14)(y + 11) = 4, where x + 24/x = y

=> y2 + 25Y + 154 = 4

=> y2 + 25y + 150 = 0

=> (y + 15)(y + 10) = 0

=> y = -15, -10

If y = -15, then

x + 24/x = -15

=> x2 + 15x + 24 = 0

=> x = [-15 ±√129]/2

If y = -10, then x + 24/x = -10

=> x2 + 10x + 24 = 0

=> (x + 4)(x + 6) = 0

=> x = -4,-6.

Hence, the ROOTS of the given equation are -4,-6, [-15 ±√129]/2.


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