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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

 

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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.1 | Q: 4 | Page no. 5
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.1 | Q: 4 | Page no. 5
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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)` Concept: Quadratic Equations.
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