Question

urgent please both 29 21​

Answer 1

Answer:

Step-by-step explanation:

(20)

Given x = (√3 +1)/2

4((√3 +1)/2)^3 + 2((√3 +1)/2)^2 − 8((√3 +1)/2) + 7

Now, 4(√3 +1)^3/8 + 2(√3 +1)^2/4 − 8(√3 +1)/2 + 7

=> (√3 +1)^3/2 + (√3 +1)^2/2 − 4(√3 +1) + 7

We know that,(a + b)^n = ∑[k=0,n] C(n,k) * a^(n−k) * b^k

Hence (a + b)^3 = 1a^3 + 3a^2b + 3ab^2 + 1b^3

and (a + b)^2 = 1a^2 + 2ab + 1b^2

=> (3√3 + 9 + 3√3 +1)/2 + (3 + 2√3 +1)/2 − 4(√3 +1) + 7

=> (6√3 + 10)/2 + (2√3 +4)/2 − 4(√3 +1) + 7

=> 3√3 + 5 + √3 + 2 − 4√3 − 4 + 7

=> 10

Answer for (20) is 10

(21)

To prove

1/(3–√8)–1/)√8–√7)+1/(√7–√6)–1/(√6–√5)+1/(√5-2)=5

Now,

1/3-√8 = 3+√8,

1/√8-√7 = √8+√7,

1/√7-√6 = √7+√6,

1/√6-√5 = √6+√5,

1/√5-2 = √5+2

∴ 1/(3–√8)–1/(√8–√7)+1/(√7–√6)–1/(√6–√5)+1/(√5–2)

= 3+√8–(√8+√7)+√7+√6–(√6+√5)+√5+2

= 3+2+√8–√8+√7–√7+√6–√6+√5–√5

=3+2 = 5

Hence proved.

Hope this helps you