If x = 3 + 2 √2, find the value of [√x - 1 (8)√x]
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Answer:
x= 3+2√2
Identity = (a+b)²= a²+b²+2ab
2√2 is 2ab part.
2√2= 2ab
ab = √2
3 must be a²+b²
possibilities of a and b
a= 1,b=√2 or vice versa
a² = 1²= 1
b²= (√2)² = 2
1+2 = 3
therefore
3+2√2 = (1+√2)²
√x = √3+2√2
= √(1+√2)²
= 1+√2
√x+1/√x
= 1+√2 +1/1+√2
1/√x=
by rationalising
1/1+√2× 1-√2/1-√2
Identity - (a+b)(a-b) = a²-b²
= (1-√2)/1²-(√2)²
= (1-√2)/1-2
(1-√2)/-1
= -(1-√2)
= -1+√2
√x+1/√x=
1+√2-1+√2
1 gets cancelled.
= 2√2.
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