5. If x=
V3+1
V3 - 1
and y =
V3 - 1
3+1
O A 10
then the value of (x2 + y2) is:
OB. 13
O C. 14
D. 15
Answers
Answered by
0
Answer :
Given that,
x = (√3 + 1)/(√3 - 1)
and y = (√3 - 1)/(√3 + 1)
So, x + y
= (√3 + 1)/(√3 - 1) + (√3 - 1)/(√3 + 1)
= {(√3+1)(√3+1)+(√3-1)(√3-1)}/(√3-1)(√3+1)
= (3 + 2√3 + 1 + 3 - 2√3 + 1)/(3 - 1)
= 8/2
= 4
So, (x + y)²
= 4²
= 16
and xy
= (√3 + 1)/(√3 - 1) × (√3 - 1)/(√3 + 1)
= (3 - 1)/(3 - 1)
= 2/2
= 1
∴ x² + y² + xy
= (x + y)² - 2xy + xy
= (x + y)² - xy
= 16 - 1
= 15
Similar questions