Question

please answer fast very urgent.

Answer 1

Answer:

93

Step-by-step explanation:

(i)

a = (√3 - √2)/(√3 + √2),

   On rationalizing, we get

   = [(√3 - √2)/(√3 + √2)] * [(√3 - √2)/(√3 - √2)]

   = (√3 - √2)²/(√3)² - (2)²

   = (3 + 2 - 2√3√2)

   = 5 - 2√6

Then,

a² = (5 - 2√6)²

   = 25 + 24 - 20√6

   = 49 - 20√6

(ii)

b = (√3 + √2)/(√3 - √2)

  On rationalizing, we get

  = [(√3 + √2)/(√3 - √2)] * [(√3 + √2)/(√3 + √2)]

  = [(√3 + √2)²/(√3)² - (2)²]

  = (3 + 2 + 2√3√2)

  = 5 + 2√6  

Then,

b² = (5 + 2√6) ²

    = 25 + 24 + 20√6

    = 49 + 20√6

Now,

ab = (5 - 2√6)(5 + 2√6)

    = (5)² - (2√6)²  [∴ (a - b)(a + b) = a² - b²]

    = 25 - 24

    = 1.

Value of a² + b² - 5ab

= (49 - 20√6) + (49 + 20√6) - 5(1)

= 49 - 20√6 + 49 + 20√6 - 5

= 98 - 5

= 93.

Hope it helps!

Answer 2

Answer:

93

Step-by-step explanation:

a = (√3-√2)/(√3+√2)

 = (√3-√2)/(√3+√2)× (√3-√2)/(√3-√2) [ rationalizing it]

 =(√3 -√2)²/1 = (√3 -√2)² = 5- 2√6

b= (√3+√2)/(√3-√2)×(√3+√2)/(√3+√2) [ rationalizing it]

 = (√3+√2)²/1 =(√3+√2)² = 5+2√6

now, a²+b² - 5ab 

= (5-2√6)² + (5+2√6)² - 5(5-2√6)(5+2√6)

=25 +24 -20√6 +25 +24 + 20√6 - 5(25-24)

=98 -5 = 93