x-a-x-b-x-c-x-d-solve-for-x-

Question Number 50730 by ajfour last updated on 19/Dec/18

\sqrt{x - a} + \sqrt{x - b} + \sqrt{x - c} + x = d

s o l v e f o r x .

Answered by behi83417@gmail.com last updated on 21/Dec/18

a f t e r s q u a r i n g a n d s y m p l i f i n g i g o t

t h i s e q u t i t i o n :

9 x^{4} + {Ax}^{3} + {Bx}^{2} + Cx + D = 0

A = - 24 (a + b) + 12 d - 10

B = 22 {(a + b)}^{2} + 8 (1 - 2 d) (a + b) - 2 d^{2} + 10 c + 1

C = - 16 {(a + b)}^{3} - 2 (1 - 2 d) {(a + b)}^{2} -

- 8 (c - 4 d^{2}) (a + b) - 2 c - 4 d c - 2 d^{2} - 4 d^{3}

D = {(a + b)}^{4} + 2 (c - d^{2}) {(a + b)}^{2} + {(c + d^{2})}^{2}

Commented by ajfour last updated on 21/Dec/18

S i r, p l e a s e c h e c k i f

a = 31, b = 47, c = 55, d = 65

w e s h o u l d g e t x = 56 .

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