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Find the positive constant k so that the equation  has a unique solution in x.

 Apr 7, 2020
edited by SpongeBobRules24  Apr 8, 2020
 #1
avatar+930 
0

When plugging in values of x that are squares, you get k to equal 2.

So your answer should be k= 2.

 

Hope it helps!

 Apr 7, 2020
 #2
avatar+1088 
+5

I'm sorry, but your answer is incorrect.

SpongeBobRules24  Apr 7, 2020
 #3
avatar+224 
+1

First square the equation and rearrange

3sqrt(x)=x+k

9x=x2+2kx+k2

0=x2+2kx-9x+k2

Factor to make it a quadratic

0=x2+(2k-9)x+k2

For a quadratic equation to have one solitution, the discrmimnant must be 0.

b2-4ac=0

Substitute in the coefficents:

(2k-9)2-4(1)(k2)=0

Expand

4k2-36k+81-4k2=0

Simplify

-36k+81=0

Solve

-4k+9=0

-4k=-9

k=2.25

 Apr 7, 2020

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