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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.

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RD Sharma Solution for Class 10 Maths (2018 (Latest))
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.