Question

please answer the 23rd and 24th questions... please! please! please!!!!!!

Answer 1

Hello Mate!

23. Since x = 2 - √3

So, 1/x = 1/( 2 - √3 )

On rationalizing we get,

= 1/( 2 - √3 ) × ( 2 + √3 )/( 2 + √3 )

= ( 2 + √3 )/( 4 - 3 ) = 2 + √3

So, keeping values in equation we get,

= ( x + 1/x )³ + 2( x + 1/x )² + ( x + 1/x ) - 100

= ( 2 - √3 + 2 + √3 )³ + 2( 2 - √3 + 2 + √3 )² + ( 2 - √3 + 2 + √3 ) - 100

= 4³ + 2(4)² + 4 - 100

= 64 + 32 + 4 - 100

= 0

24. So, on keeping value of x as - 2 and - 1 in x³ + 8x² + 17x + ax we get same remainder so,

p(x) = x³ + 8x² + 17x + ax

p(x) = (-2)³ + 8(-2)² + 17(-2) + a(-2)

p(x) = - 8 + 32 - 34 - 2a

p(x) = - 10 - 2a

Now,

p(x) = x³ + 8x² + 17x + ax

p(x) = (-1)³ + 8(-1)² + 17(-1) + a(-1)

p(x) = - 1 + 8 - 17 - a

p(x) = - 10 - a

Since reminder are same so,

- 10 - 2a = - 10 - a

0 = - a + 2a

0 = a

Hence value of a is "0".

Have great future ahead!

Answer 2

q 23 and q 24 refer the attachment