Question

if x = root 3 + root 2 by root 3 - root 2 and y equals to root 3 root- 2 by root 3 + root 2 find X square + Y square answer should be X square + Y square = 90​

Answer 1

Answer:

this is your solution for the following information

Answer 2

Answer:

98 is the value of $x^2 + y^2$.

Step-by-step explanation:

Explanation:

Given in the question,

x = $\frac{\sqrt{3} + \sqrt{2} }{\sqrt{3} -\sqrt{2} }$ and y = $\frac{\sqrt{3} - \sqrt{2} }{\sqrt{3} +\sqrt{2} }$

First we rationalize the give values of x and y .

• Rationalization- A defence strategy known as rationalisation involves providing what appear to be logical justifications for actions that are actually driven by unconscious instinctive urges.

• It is an effort to identify the causes of behaviour, particularly one's own.

Step 1:

We have x = $\frac{\sqrt{3} + \sqrt{2} }{\sqrt{3} -\sqrt{2} }$  .........(i)and y = $\frac{\sqrt{3} - \sqrt{2} }{\sqrt{3} +\sqrt{2} }$ .........(ii)

On multiplying numerator and denominator by $\frac{\sqrt{3} + \sqrt{2} }{\sqrt{3} +\sqrt{2} }$ in (i) we get,

⇒ $\frac{\sqrt{3} + \sqrt{2} }{\sqrt{3} -\sqrt{2} } .\frac{\sqrt{3} +\sqrt{2} }{\sqrt{3} +\sqrt{2} }$

⇒$\frac{(\sqrt{3} + \sqrt{2})^2 }{(\sqrt{3} -\sqrt{2})(\sqrt{3} + \sqrt{2} )}$

⇒$\frac{3 + 2 + 2\sqrt{6} }{3 - 2}$ = 5 + $2\sqrt{6}$

Similarly on multiplying numerator and denominator by $\frac{\sqrt{3} - \sqrt{2} }{\sqrt{3} -\sqrt{2} }$.

⇒ $\frac{\sqrt{3} - \sqrt{2} }{\sqrt{3} +\sqrt{2} }.\frac{\sqrt{3} - \sqrt{2} }{\sqrt{3} -\sqrt{2} }$

⇒ $\frac{(\sqrt{3} - \sqrt{2} )^2}{(\sqrt{3} +\sqrt{2})(\sqrt{3}-\sqrt{2} ) }$ = $\frac{3 +2 - 2\sqrt{6} }{3 - 2}$ = 5 - $2\sqrt{6}$.

Step 2:

Now, from step 1,

x = 5 + $2\sqrt{6}$ and y =  5 - $2\sqrt{6}$.

According to the question we need to find the value of $x^2 + y^2$.

From step 1, put the value of x and y,

$x^2 + y^2$

⇒$(5 + 2\sqrt{6} )^2$ +  $(5 - 2\sqrt{6} )^2$

⇒25 + 4 .(6) + 2 ×$2\sqrt{6}$ × 5 + 25 + 4 (6) - 2 ×$2\sqrt{6}$ × 5.

⇒25 + 24 + 25 + 24 = 50 + 48

⇒ 98

Final answer:

Hence, the value of $x^2 + y^2$ is 98.

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