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x-7sqrt(x)+10=0 . the solution set is/are x = ?. is there an extraneous solution? if so what is / are x=?

math algebra
Guest Aug 27, 2014

Best Answer 

 #1
avatar+90988 
+10

Mmm interesting

x-7sqrt(x)+10=0

Let y=sqrt(x) then we have

y^2-7y+10=0

(y-2)(y-5)=0

y=2 or 5

$$\\\sqrt x = 2 \;or\; 5\\
x=4 \;or \;25\\\\
check\; x=4\\
4-7*2+10=0 \;true\\
check x=25\\
25-35+10=0 \;true\\\\
So\; x=4\; or\; x=25$$

Melody  Aug 27, 2014
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1+0 Answers

 #1
avatar+90988 
+10
Best Answer

Mmm interesting

x-7sqrt(x)+10=0

Let y=sqrt(x) then we have

y^2-7y+10=0

(y-2)(y-5)=0

y=2 or 5

$$\\\sqrt x = 2 \;or\; 5\\
x=4 \;or \;25\\\\
check\; x=4\\
4-7*2+10=0 \;true\\
check x=25\\
25-35+10=0 \;true\\\\
So\; x=4\; or\; x=25$$

Melody  Aug 27, 2014

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