?
If x = 1 + √2 + √3, then find the value of x2 - 2x + 4.
Answer & Solution
Correct Answer:
Option
B
x = 1 + √2 + √3
⇒ x - 1 = √2 + √3
On squaring both sides,
(x - 1)2 = (√2 + √3)2
⇒ x2 - 2x + 1 = 2 + 3 + 2√6
Add 3 both side
⇒ x2 - 2x + 4 = 5 + 2√6 + 3
⇒ x2 - 2x + 4 = 8 + 2√6
⇒ x2 - 2x + 4 = 2(4 + √6)
⇒ x - 1 = √2 + √3
On squaring both sides,
(x - 1)2 = (√2 + √3)2
⇒ x2 - 2x + 1 = 2 + 3 + 2√6
Add 3 both side
⇒ x2 - 2x + 4 = 5 + 2√6 + 3
⇒ x2 - 2x + 4 = 8 + 2√6
⇒ x2 - 2x + 4 = 2(4 + √6)
Join the Discussion
Login to post a comment or share your explanation.
Login