Question

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Answer 1

EXPLANATION

1) = x = √5 + 2

TO PROVE.

x^2 + 1/x^2 = 18

if x = √5 + 2

therefore,

1/x = 1/√5 + 2

rationalise the term

1/√5 + 2 X √5 - 2 / √5 - 2

√5 - 2 / 5 - 4

√5 - 2

put the value of x and 1/x in equation

(√5 + 2 )^2 + (√5 - 2)^2

5 + 4 + 4√5 + 5 + 4 - 4√5

9 + 9 = 18

HENCE PROVED.

2) = (x - 1)(x - 2 ) is a factor of polynomial

x^3 - x^2 - 4x + 4

SHOW THAT (X - 1 )(X - 2 ) IS A FACTOR

OR NOT.

(x - 1 ) = 0

x = 1

put x = 1 in above equation

we get,

(1)^3 - (1)^2 - 4(1) + 4

1 - 1 - 4 + 4

= 0

( x - 2)

x - 2 = 0

x = 2

(2)^3 - (2)^2 - 4(2) + 4

8 - 4 - 8 + 4

= 0

HENCE PROVED

NOTE = ALSO SEE THE ATTACHMENT.

Answer 2

Answer:

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