If x^2 +1 /X^2 = 51, find x-1 / x
Answers
Step-by-step explanation:
x
2
+
x
2
1
\bold{And\: We \:Need \:To\: Find...}AndWeNeedToFind...
\bold{{x} - \frac{1}{x}}x−
x
1
So Now Let's Move For Solution ....
\underline{\bold{Solution}}
Solution
Now According To Question It's Given That {x}^{2} + \frac{1}{ {X}^{2} } = 51x
2
+
X
2
1
=51
Now To Find ...
\bold{x - \frac{1}{x}}x−
x
1
Follow The Simple Step ...
\underline{\bold{Step-1)\:Find\:The\: Suitable\: Identity\:}}
Step−1)FindTheSuitableIdentity
So The MosT Suitable Identity That Can Be Used Here Is...
\boxed{\bold{{(a - b)}^{2} \:= {a}^{2} \:+ \:{b}^{2} -2ab}}
(a−b)
2
=a
2
+b
2
−2ab
\underline{\bold{Step-2)\:Apply\: The \:Identity\: To \: Find\: Value \:Of\:\:{x}\:- \frac{1}{x} }}
Step−2)ApplyTheIdentityToFindValueOfx−
x
1
Now Applying This Identity ..
Where
\underline{\bold{a\: = \:x \:\:And\: b \:= 1/x \:}}
a=xAndb=1/x
\bold{ {(x\: - \:\frac{1}{x})}^{2} = \: {x}^{2} \:+ \:\frac{1}{ {x}^{2} } - 2(x) (\frac{1}{x} )}(x−
x
1
)
2
=x
2
+
x
2
1
−2(x)(
x
1
)
That Is ...
\bold{{(x - \frac{1}{x})}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } \: - 2 \: (by \: \: \: cancelling \: x)}(x−
x
1
)
2
=x
2
+
x
2
1
−2(bycancellingx)
So Now In Question Its Given That
\bold{ {x}^{2} + \frac{1}{ {x}^{2} }}x
2
+
x
2
1
Now Putting This Value In the Obtained Equation We Have ...
\bold{ {(x - \frac{1}{x}) }^{2} = 51 - 2}(x−
x
1
)
2
=51−2
That Is ...
\bold{ {(x - \frac{1}{x} )}^{2} = 49}(x−
x
1
)
2
=49
Now Moving Square To RHS We Have
\bold{x - \frac{1}{x} = \sqrt{49}}x−
x
1
=
49
That Is ...
\bold{x - \frac{1}{x} = 7}x−
x
1
=7
So Now We Have Value Of
\boxed{\bold{x - \frac{1}{x} = 7}}
x−
x
1
=7
\underline{\bold{Hence\:The\: Required\:Answer\:Is\:....}}
HenceTheRequiredAnswerIs....
\boxed{\boxed{\bold{7}}}
7
\Large{\bold{Thanks...}}Thanks...
Step-by-step explanation:
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