Question

pls.... give me the right solution of this Question

Answer 1

given p = $\bold{\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}}$

p = $\bold{\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}}$ * $\bold{\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2}}}$

p = $\bold{\frac{(\sqrt{3} + \sqrt{2})^2}{3 - 2}}$
$\bold{\to\to\to\to\to\to\to\to \therefore\boxed{(a - b)(a + b) = (a^2 - b^2)}}$

p = (3 + 2 + 2√6)

p² = (5 + 2√6)²

p² = (25 + 24 + 20√6)

p² = (49 + 20√6)--------------( 1 )

similarly,

q = $\bold{\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}}$ * $\bold{\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}}$

q = $\bold{\frac{(\sqrt{3} - \sqrt{2})^2}{3 - 2}}$ $\bold{\to\to\to\to\to\to\to\to\therefore\boxed{(a - b)(a + b) = (a^2 - b^2)}}$

q = (3 + 2 - 2√6)

q = (5 - 2√6)

q² = (25 + 49 - 20√6)

q² = (49 - 20√6)-------------( 2 )

adding-----------( 1 ) & ------------( 2 )

p² + q² = (49 + 20√6) + (49 - 20√6)

p² + q² = 49 + 49

hence, the value of p² + q² = 98

Answer 2

Answer:

98

Step-by-step explanation:

Consider the given question. First taking

P =  √3 + √2 / √3 - √2

Rationalizing the denominator we have

P =  √3 + √2 / √3 - √2  x   √3 + √2 / √3 + √2

here by using the formula (a^2 - b^2) = (a + b)(a - b)

Now we get (√3 + √2 )^2 / 3 - 2

P = (√3 + √2 )^2

here using the formula (a+ b)^2 = a^2 + 2ab + b^2

P = 3 + 2√6 + 2

P = 5 + 2√6

Similarly we can take up for q also.

Q = √3 - √2 / √3 + √2

Rationalizing the denominator we get

Q = √3 - √2 / √3 + √2  x   √3 - √2 / √3 - √2

Q = (√3 - √2)^2 / 3 - 2

Q = (√3 - √2 )^2

here by using the formula (a - b)^2 = a^2 - 2ab + b^2

Q = 3 - 2√6 + 2

Q = 5 - 2√6

They have asked to find P^2 + Q^2

So P ^2 + Q^2 = (5 + 2√6)^2 + (5 - 2√6)^2

Since we know the formula for (a + b)^2 and (a - b)^2 . Applying it we get

 25 + 20√6 + 24 + 25 - 20√6 + 24

 50 + 48 = 98