if x = 3+2√2 find 1÷x²
Answers
Answered by
1
Answer:
1/7
Step-by-step explanation:
1/(3+2√2)²
1/7
The value of (3+2√2)²=7
Answered by
1
If x = 3 +2√2, then 1/x = 1/(3+2√2) =(3–2√2), because 3^2 -(2√2)^2 =9–8=1. Hence x^2 +(1/x^2) = [x+(1/x)]^2 -2 = 6^2 -2 =36 -2 = 34.
x=3+2√2
Inverse equatio,
1/x=1/3+2√2
=>1/x=(3–2√2){(3+2√2)(3–2√2)}
=>1/x=(3–2√2)/{(3)²-(2√2)²}
=>1/x=(3–2√2)/(9–8)
=>1/x=(3–2√2)/1
=>1/x=3–2√2
=>x+1/x=3+2√2+3–2√2
=>x+1/x=6
=>x²+1/x²=(x+1/x)² -2.x.1/x
=>x²+1/x² =(6)²-2
=>x²+1/x²=36–2
=>x²+1/x²=34
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