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Question

# Solve the equation √2x−6+√x+4=5

A
2
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B
4
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C
5
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D
8
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Solution

## The correct option is C 5√2x−6+√x+4=5 Here 2x−6>0 means x>3and also x+4>0 which means x>−4 x need to satisfy these conditions also⇒ √2x−6=−√x+4+5 ----- ( 1 )⇒ (√2x−6)2=(−√x+4+5)2 [ Squaring both sides ]⇒ 2x−6=x+4+25−10√x+4⇒ 10√x+4=−2x+6+x+4+25⇒ 10√x+4=−x+35⇒ (10√x+4)2=(−x+35)2 [ Squaring both sides ]⇒ 100x+400=x2−70x+1225⇒ x2−170x+825=0⇒ x2−165x−5x+825=0⇒ x(x−165)−5(x−165)=0⇒ (x−165)(x−5)=0∴ x=165 or x=5Now substitute x=165 in equation (1 ),⇒ √(2×165)−6=−√(165)+4+5⇒ √324=−8⇒ 18≠−8Now substituting x=5 in equation ( 1 ),⇒ √(2×5)−6=√5+4+5⇒ √4=2∴ 2=2∴ Solution is x=5

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