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In the Following, Determine Whether the Given Values Are Solutions of the Given Equation Or Not: A2x2 - 3abx + 2b2 = 0, `X=A/B`, `X=B/A` - Mathematics

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Question

In the following, determine whether the given values are solutions of the given equation or not:

a2x2 - 3abx + 2b2 = 0, `x=a/b`, `x=b/a`

Solution

We have been given that,

a2x2 - 3abx + 2b2 = 0, `x=a/b`, `x=b/a`

Now if `x=a/b` is a solution of the equation then it should satisfy the equation.

So, substituting `x=a/b` in the equation, we get

a2x2 - 3abx + 2b2

`=a^2(a/b)^2-3ab(a/b)+2b^2`

`=(a^4-3a^2b^2+2b^4)/b^2`

Hence `x=a/b` is not a solution of the quadratic equation.

Also, if `x=b/a` is a solution of the equation then it should satisfy the equation.

So, substituting `x=b/a` in the equation, we get

a2x2 - 3abx + 2b2

`=a^2(b/a)^2-3ab(b/a)+2b^2`

= b2 - 3b2 + 2b2

= 0

Hence `x=b/a` is a solution of the quadratic equation.

Therefore, from the above results we find out that `x=a/b` is not a solution and `x=b/a` is a solution of the given quadratic equation.

  Is there an error in this question or solution?
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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.1 | Q: 2.7 | Page no. 4
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.1 | Q: 2.7 | Page no. 4
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In the Following, Determine Whether the Given Values Are Solutions of the Given Equation Or Not: A2x2 - 3abx + 2b2 = 0, `X=A/B`, `X=B/A` Concept: Quadratic Equations.
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