How do you solve sqrt(20-X) + 8= sqrt( 9-X) +11√20−X+8=√9−X+11?

2 Answers
Johnson Z.
May 19, 2016

x=80/9x=809

Explanation:

Given,

sqrt(20-x)+8=sqrt(9-x)+11√20−x+8=√9−x+11

Subtract 88 from both sides.

sqrt(20-x)+8color(white)(i)color(red)(-8)=sqrt(9-x)+11color(white)(i)color(red)(-8)√20−x+8i−8=√9−x+11i−8

sqrt(20-x)=sqrt(9-x)+3√20−x=√9−x+3

Square both sides to get rid of the radical signs.

(sqrt(20-x))^2=(sqrt(9-x)+3)^2(√20−x)2=(√9−x+3)2

(sqrt(20-x))(sqrt(20-x))=(sqrt(9-x)+3)(sqrt(9-x)+3)(√20−x)(√20−x)=(√9−x+3)(√9−x+3)

Simplify.

20-x=(9-x)+6sqrt(9-x)+920−x=(9−x)+6√9−x+9

20-x=9-x+6sqrt(9-x)+920−x=9−x+6√9−x+9

2=6sqrt(9-x)2=6√9−x

Solve for xx.

1/3=sqrt(9-x)13=√9−x

(1/3)^2=(sqrt(9-x))^2(13)2=(√9−x)2

1/9=9-x19=9−x

x=color(green)(|bar(ul(color(white)(a/a)color(black)(80/9)color(white)(a/a)|)))

Cesareo R.
May 19, 2016

x = 80/9

Explanation:

Regrouping and powering
(sqrt[20 - x] - sqrt[9 - x])^2 =(11 - 8)^2
giving
29 - 2 sqrt[9 - x] sqrt[20 - x] - 2 x = 9
Regrouping and powering
(2 sqrt(9 - x) sqrt(20 - x))^2 =(29 - 9 - 2 x)^2
giving
9x=80
Solving for x we get x = 80/9

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