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Question

The number of real roots of x2x6+6x25x39=x2+4x21 is?

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is A 1
x2x6+6x25x39=x+4x21
squaring on both sides:
(x2x6)+(6x25x39)+2(x2x6)(6x25x39)=x2+4x21
2x2x66x25x39=6x2+10x+24
Again, squaring on both sides,
4(x2x6)(6x25x39)=(6x2+10x+24)2
24x444x3280x2+276x+936=36x4120x3188x2+480x+576
12x4+76x396x2240x+360=0
4(x3)2(x2)(3x+5)=0
x=3,2,53
But only x=3 satisfies the equation.
The number of real roots is 1.

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