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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

5. Radical Equations

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Exercise 36 Page 262

Square both sides of the radical equation to eliminate the radicals.

x=3

Practice makes perfect

We will start solving the given radical equation by squaring both sides to eliminate the radicals.

sqrt(x+9)=sqrt(3)+sqrt(x)

LHS^2=RHS^2

(sqrt(x+9))^2=(sqrt(3)+sqrt(x))^2

ExpandPosPerfectSquare

(a+b)^2=a^2+2ab+b^2

(sqrt(x+9))^2=(sqrt(3))^2+2sqrt(3)sqrt(x)+(sqrt(x))^2

( sqrt(a) )^2 = a

x+9=3+2sqrt(3)sqrt(x)+x

sqrt(a)*sqrt(b)=sqrt(a* b)

x+9=3+2sqrt(3x)+x

LHS-x=RHS-x

9=3+2sqrt(3x)

LHS-3=RHS-3

6=2sqrt(3x)

.LHS /2.=.RHS /2.

3=sqrt(3x)

LHS^2=RHS^2

9=(sqrt(3x))^2

( sqrt(a) )^2 = a

9=3x

.LHS /3.=.RHS /3.

3=x

Rearrange equation

x=3

Subchapter links

Exercises p.261-263