Question

If sqrt(a)x-sqrt(b)v=b-a and sqrt(b)x-sqrt(a)v=0 .then the value of x .y is: (a) a+b (b) a-b (c) sqrt(ab) (d) -sqrt(ab)​

Answer 1

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Given Equation :

To calculate :

Value of a and b.

Clarification :

In order to calculate the value of a and b, firstly we need to rationalize the denominator in L.H.S. After that, by comparing L.H.S and R.H.S, we'll finr the value of a and b.

How to rationalize the denominator ?

To rationalize the denominator, we simply multiply the numerator and the denominator with the rationalizing factor of the denominator.

After that, by using algebraic identities, we simplify further.

Explication of steps :

Rationalising the denominator in LHS :

Rationalizing factor of (a - b) is (a + b). So, rationalizing factor of (3√2 - 2√3) is (3√2 + 2√3).

As we know that,

(a - b)(a + b) = a² - b²

Now, in RHS we have :

From, LHS and RHS, we have :

Step-by-step explanation: