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namitasharma34:
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Given x = 3 + 2√2 ⇒ x2 = 17 + 12√2 ⇒ 1/x2 = 1/(17 + 12√2)
On rationalizing the denominator we get
1/x2 = (17 – 12√2)
∴ (x2+1/x2) =(17 + 12√2) + (17 – 12√2) = 34
On rationalizing the denominator we get
1/x2 = (17 – 12√2)
∴ (x2+1/x2) =(17 + 12√2) + (17 – 12√2) = 34
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Answered by
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From the question , we have
x = 3- 2√2
→1/x = 1/(3-2√2)
→1/x = 1(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 .
Now ,
(x^2 + 1/x^2 -34 )= (x^2+1/x^2 -2-32)= (x-1/x) ^2 -32 = ( 3-2√2 - 3- 2√2 )^2-32= ( -4√2)^2-32= 32-32=0
I hope , it helps you dear mate .
x = 3- 2√2
→1/x = 1/(3-2√2)
→1/x = 1(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 .
Now ,
(x^2 + 1/x^2 -34 )= (x^2+1/x^2 -2-32)= (x-1/x) ^2 -32 = ( 3-2√2 - 3- 2√2 )^2-32= ( -4√2)^2-32= 32-32=0
I hope , it helps you dear mate .
thank you
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