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# Determine If, 3 is a Root of the Equation Given Below: Sqrt(X^2-4x+3)+Sqrt(X^2-9)=Sqrt(4x^2-14x+16) - Mathematics

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#### Question

Determine if, 3 is a root of the equation given below:

sqrt(x^2-4x+3)+sqrt(x^2-9)=sqrt(4x^2-14x+16)

#### Solution

Given to check whether 3 is a root of the equation

sqrt(x^2-4x+3)+sqrt(x^2-9)=sqrt(4x^2-14x+16)

Here LHS = sqrt(x^2-4x+3)+sqrt(x^2-9) and RHS = sqrt(4x^2-14x+16)

Substitute x = 3 in LHS

rArrsqrt(3^2-4(3)+3)+sqrt(3^2-9)

rArrsqrt(9-18+3)+sqrt(9-9)

rArrsqrt0+sqrt0

⇒ 0

∴ LHS = 0

Similarly, substitute x = 3 in RHS.

rArrsqrt(4(3)^2)-14(3)+16

rArrsqrt(4xx9-42+16)

rArrsqrt(36-42+16)

rArrsqrt(52-42)

rArrsqrt10

∴ RHS =sqrt10

Now, we can observe that

LHS ≠ RHS

∴ x = 3 is not a solution or root for the equation

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Determine If, 3 is a Root of the Equation Given Below: Sqrt(X^2-4x+3)+Sqrt(X^2-9)=Sqrt(4x^2-14x+16) Concept: Quadratic Equations.