SOLUTION: re-post questions 1. √x-1=3 2. √x^3=8 3. 3√x^2=4 4. Is an identity (true for all values of x)? Answer and explain

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: re-post questions 1. √x-1=3 2. √x^3=8 3. 3√x^2=4 4. Is an identity (true for all values of x)? Answer and explain       Log On


   

Question 25018: re-post questions
1. √x-1=3
2. √x^3=8
3. 3√x^2=4
4. Is an identity (true for all values of x)?
Answer and explain
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
1. √x-1=3
√x=3+1=4..SQUARING BOTH SIDES
X=4*4=16
2. √x^3=8
√x=8^(1/3)=2...SQUARING BOTH SIDES
X=2*2=4
3. 3√x^2=4..ASSUMING YOU MEANT (3√x)^2=4
9X=16..OR X=16/9
...OR.....ASSUMING YOU MEANT 3(√x)^2=4
3X=4..OR...X=4/3
4. Is an identity (true for all values of x)?
YES IDENTICAL OR CONGRUENT MEANS TRUE FOR ALL VALUES OF X
FOR EXAMPLE
(X+A)^2=X^2+A^2+2*X*A...FOR ALL VALUES OF X AND A .THIS IS AN IDENTITY.YOU CAN TEST BY TAKING DIFFERENT VALUES FOR X AND A.SAY 1,2,3 ETC..
ON THE OTHER HAND X+3=4 AND X^2=4 ARE NOT IDENTITIES ...IT IS ONLY TRUE FOR A CERTAIN VALUE / OR SOME OR MANY VALUES VALUES OF X BUT NOT ALL VALUES OF X.HERE
X+3=4 IS TRUE ONLY FOR X=1
X^2=4 IS TRUE ONLY FOR X= +2 AND -2
SIMILARLY X+A=10 IS TRUE FOR MANY VALUES OF X BUT NOT FOR ALL VALUES OF X ...IF A=4 THEN X=6...IF A=2 THEN X=8 ETC...