x-y-a-z-bx-c-bz-xy-d-Find-yz-in-terms-of-a-b-c-d-

Question Number 54595 by ajfour last updated on 07/Feb/19

x + y = a

z + b x = c

b z + x y = d

F i n d y z i n t e r m s o f a, b, c, d .

Commented by mr W last updated on 07/Feb/19

y = a - x

z = c - b x

b (c - b x) + x (a - x) = d

x^{2} + (b^{2} - a) x + d - b c = 0

x = \frac{a - b^{2} \pm \sqrt{{(b^{2} - a)}^{2} - 4 (d - b c)}}{2}

y z = (a - x) (c - b x)

\Rightarrow y z = \frac{[a + b^{2} \pm \sqrt{{(b^{2} - a)}^{2} - 4 (d - b c)}] [2 c + b^{3} - a b \pm b \sqrt{{(b^{2} - a)}^{2} - 4 (d - b c)}]}{4}

Commented by ajfour last updated on 07/Feb/19

T h a n k s S i r, b u t w e c a n m a k e u s e

o f e q . i n x^{2} o n l y t o g e t x^{2} i n t e r m s

o f x a n d t h e n s u b s t i t u t e, d o i n g t h i s

i g e t y z = a c + b^{2} c - b d - (c + b^{3}) x

i g e t y z = a c + b^{2} c - b d

- (c + b^{3}) \frac{a - b^{2} \pm \sqrt{{(b^{2} - a)}^{2} - 4 (d - b c)}}{2} .

Commented by mr W last updated on 07/Feb/19

r i g h t s i r .

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