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If X =`(Sqrt(A + 3b) + Sqrt(A - 3b))/(Sqrt(A + 3b) - Sqrt(A - 3b)) Prove that `3bx^2 - 2ax + 3b = 0 - ICSE Class 10 - Mathematics

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Question

If x = `(sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))` prove that `3bx^2 - 2ax + 3b = 0`

Solution

Since `x/1 = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`

Applying componendo and dividendo we get

`(x + 1)/(x - 1) = (sqrt(a + 3b) + sqrt(a - 3b) + sqrt(a + 3b) - sqrta - 3b)/(sqrt(a + 3b) + sqrt(a - 3b) - sqrt(a + 3b) + sqrt(a - 3b))`

`(x + 1)/(x - 1)= (2sqrt(a + 3b))/(2sqrt(a - 3b))`

Squaring both sides.

Again applying componendo and dividendo

`(x^2 + 2x + 1 + x62 - 2x + 1)/(x^2 + 2x + 1 - x^2 + 2x - 1) = (a + 3b + a - 3b)/(a + 3b - a + 3b)`

`(2(x^2 + 1))/(2(2x)) = (2(a))/(2(3b))`

`3b(x^2 + 1) = 2ax`

`3bx^2 - 2ax + 3b = 0`

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 Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 7: Ratio and Proportion (Including Properties and Uses)
Ex.7C | Q: 12

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Solution If X =`(Sqrt(A + 3b) + Sqrt(A - 3b))/(Sqrt(A + 3b) - Sqrt(A - 3b)) Prove that `3bx^2 - 2ax + 3b = 0 Concept: Proportions.
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