SOLUTION: Find the real solutions of each equation.
31. the sqrt of 10 + 3 and within this sqrt is the sqrt of x = the sqrt of x
33. (3x +1) to the power of 1/2 = 4
39. x to the pow
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Question 182180: Find the real solutions of each equation.
31. the sqrt of 10 + 3 and within this sqrt is the sqrt of x = the sqrt of x
33. (3x +1) to the power of 1/2 = 4
39. x to the power of 3/2 - 3x to the power of 1/2 = 0
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
31. I think you mean:
Square both sides:
Add -10 to both sides:
Square both sides:
(x - 25) = 0)
Check answers:
is extraneous
is valid.
33.
^{\frac{1}{2}} = 4)
This is exactly the same as:
Just square both sides and solve.
39. Two possible interpretations:
 }\math x^{3 \over 2} - 3x^{1 \over 2} = 0\ \ \Rightarrow\ \ x^{3 \over 2} = 3x^{1 \over 2} \cr \text{ }\math\ \ \Rightarrow\ \ x^3 = 3x \ \ \Rightarrow\ \ x^2 = 3\ \ \Rightarrow\ \ x = \pm sqrt{3})
 }\math x^{3 \over 2} - (3x)^{1 \over 2} = 0\ \ \Rightarrow\ \ x^{3 \over 2} = (3x)^{1 \over 2} \cr \text{ }\math\ \ \Rightarrow\ \ x^3 = 9x \ \ \Rightarrow\ \ x^2 = 9\ \ \Rightarrow\ \ x = \pm 3)
John
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