SOLUTION: I have a couple of questions that I am stuck with... (1/4x+3)squared = 48 options are A.{-12+16 suared root3}, -12-16squareroot 3} B.{12+16square root 3, 12-16square roo

Question 239948: I have a couple of questions that I am stuck with...
(1/4x+3)squared = 48
options are
A.{-12+16 suared root3}, -12-16squareroot 3}
B.{12+16square root 3, 12-16square root 3}
C.{16squareroot3 - 12, 16square root 3+12}
D.{-3+4square root3 over 4, -3-4square root 3 over 4}
Square root 3x+10 = 5 - 2x
options are
A. 3/4
B. 5/4, 9
C. 5
D.3/4, 5
Last one is
square root 2x+5 - square root x-2 = 3
Please help. Thank you
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
(X/4+3)^2=48
X^2/16+3X/2+9=48
X^2/16+3X/2=48-9
(X^2+3X*8)/16=39
X^2+24X=624
X^2+24X-624=0

X=(-24+-SQRT[24^2-4*1*-624])/2*1
X=(-24+-SQRT[576+2496])/2
X=(-24+-SQRT3072)/2
X=(-24+-55.426)/2
X=(-12+-16SQRT3) ANSWER A).
-------------------------------------------
Square root 3x+10=5-2x
SQRT(3X+10)=5-2X SQUARE BOTH SIDES
3X+10=(5-2X)^2
3X+10=25-20X+4X^2
4X^2-20X-3X+25-10=0
4X^2-23X+15=0
(4X+3)(X-5)=0
4X+3=0
4X=-3
X=-3/4 ANS.
X-5=0
X=5 ANS.
SOLUTION (3/4,5) ANSWER D)
-----------------------------------
square root 2x+5 - square root x-2 = 3
SQRT(2X+5)-SQRT(X-2)=3 SQUARE BOTH SIDES.
2X+5+X-2=9
3X=9-5+2
3X=6
X=6/3
X=2 ANS.
PROOF:
SQRT(2*2+5)-SQRT(2-2)=3
SQRT(4+5)-0=3
SQRT9=3
3=3

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