Solve please and Thank you

Question

Solve (Show all work)

 

√11-x= x+1

Answer 1

√11-x= x+1  add x to both sides and get √11=2x+1 , subtracting 1 from both sides  that -1+√11=2x or that

x=(-1+√11)/2

Answer 2

Do you mean square root of(11-x) ?

If so, [square root(11-x)]^2=(x+1)^2

11-x=x^2+2x+1

11=x^2+3x+1

0=x^2+3x-10

x^2+3x-10=0

(x+5)(x-2)=0

x+5=0, x=-5

x-2=0, x=2

check: SQRT(11-(-5))=SQRT(16)=4 and x+1=-5+1=-4 but SQRT symbol means principal root

(the nonnegative root)

we don't use -5 as a solution

SQRT(11-2)=SQRT(9)=3 and x+1=2+1=3

we use x=2 as a solution

Answer 3

(11)^½ - x = x + 1

 

Add x to each side of the equation:

 

(11)^½ = 2x + 1

 

Subtract 1 from each side of the equation:

 

(11)^½ - 1 = 2x

 

2x = (11)^½ - 1 = 3.317 - 1 = 2.317

 

∴x = 1.158