find x+1/x , if x² + 1/x²= 62
Answers
Step-by-step explanation:
x² + 1/x² = 62
add 2 both sides of the equation
x² + 1/x² + 2 = 62 + 2
x² + 1/x² + 2 × x² × 1/x² = 64
( x + 1/x )² = 8²
x + 1/x= ± 8
Answer:
Step-by-step explanation:
X * X + 1 ) /(X*X) = 83
=> [ (X*X) / (X*X) ] + [ 1 / (X*X) ] = 83
=> 1 + [ 1 / (X*X) ] = 83
=> [ 1 / [ X*X] ]=82 ——————————-(A)
=> (X*X) = [ 1 /82 ]
square root both side we get
=> X = ± (1/ √82)
=> 1 / X = ± (√82) ———————————-(B)
Now
(X*X*X + 1 ) / (X*X*X)
=> [ (X*X*X) / (X*X*X) ] + [ 1 / (X*X*X) ]
=> 1 + [ 1 / (X*X*X) ]
=> 1 + [ 1 / ( (X*X) *X) ]
=> 1 + [ ( 1 / ( (X*X) ) * (1 / X) ]
=> 1 + [ ( 82) * ( ± (√82) ) ] ——————————-From A and B
=> 1 ± [ 82 * (√82) ]
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Padmini Kalyanaraman, School Teacher
Answered March 5, 2018
(x+1/x)^2= x^2+2+1/x^2
(x+1/x)^2= x^2+1/x^2 +2
(x+1/x)^2= 83 +2 ( substituting the given value)
(x+1/x)^2=85
Square root of (x+1/x)^2= + or - √85
x+1/x= + or - √85
x^3+1/x^3=[ (x+1/x)( x^2 -1+1/x^2)]
x^3+1/x^3= [(x+1/x)( x^2+1/x^2–1)]
x^3+1/x^3 = +or - √85(83–1)
x^3+ 1/x^3= + or - √85(82)
x^3+1/x^3= +√85*82 or -√85 *82
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Hope this helps ☺️
Edit 1 : Corrected a mistake in the solution.
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Related Questions
More Answers Below
If x²+1/x² = 69 then what is the value of x⁴+1/x⁴?
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Subhasish Debroy, Former SDE at Bharat Sanchar Nigam Limited
Answered February 26, 2018
x^2 +1/x^2 =83, => (x+1/x)^2 -2x.1/x =83
or, (x+1/x)^2 = 83+2 =85
or, (x+1/x) = ±√(85)
Now, x^3 + 1/x^3= (x+1/x)^3 -3*x*1/x(x+1/x)
=> (±√85)^3 - 3*(±√85) = 82√85 , - 82√85
x^2 + 1/x^2 = 83 or, x^2 + 1/x^2 + 2.x.1/x = 83+2
or, (x + 1/x)^2 = 85 or, x + 1/x = √85
now x^3 + 1/x^3 = (x + 1/x)^3 - 3.x.1/x.(x + 1/x) = (√85)^3 - 3.√85 = 82√85
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