Question

Please solve this. Correctly. Please fast full process. I will give brainlist. I have the answer so don’t give wrong solution. I want to know process. Please

Answer 1

Answer:

13. a = 6/5, b = 1/5

14. x + 1/x = 2√2

Step-by-step explanation:

13. (√11-1)/(√11+1)=(√11-1)*(√11-1)/(√11+1)(√11-1)

=(11+1-2√11)/(11-1)

=(12-2√11)/10

=(6/5 - √11/5)= a - b√11

On comparing,

a = 6/5, b = 1/5

14. x^4 + 1/x^4 = 34

(x^2 + 1/x^2)^2 = x^4 + 1/ x^4 + 2 = 34 + 2 = 36

x^2 + 1/x^2 = 6 (LHS>0)

(x + 1/x)^2 = x^2 + 1/x^2 + 2 = 6 + 2 = 8

x + 1/x = 2√2 (x>1)

Answer 2

Answer:

13. a=6/5, b= 1/5

14. x+1/x=2√2

Step-by-step explanation:

13. ( √11 -1) /(√11-1) = a - b√11

LHS = ( √11 -1) ( √11 -1) / ( √11 -1)(√11+1)

=(11+1-2√11) / (11-1)

=(12-2√11)/10

=12/10-2/10√11

=6/5 -1/5√11 = a - b√11

On comparison we get

a=6/5, b= 1/5

======================

14.x⁴+1/x⁴=34

adding 2 both sides

x⁴+2*x²*1/x²+1/x⁴=34+2

(x²+1/x²)²=36

x²+1/x²=6

adding 2 both sides

x²+ 2*x*1/x +1/x² = 6+2

(x+1/x)²=8

x+1/x=√8=2√2

so x+1/x=2√2