If a=v2+1, find the value of (a-1/a)²
Answers
Answer:
How can I solve the following problem: If a-1/a=5, then a^2-1/a^2=?
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Ajay Tiwari
Answered 2 years ago
supposed to be the right answer in one method,
If a-1/a=5 the a-1=5a
-1=5a-a which is -1=4a which is a=-1/4 ————1
a²-1/a² is (-1/4)² -1/(-1/4)² which is 1/16 -1/1/16.
-15/16 / 1/16
Applying another method from given condition in problem.
Other right answer is a-1/a=5—Eq1
So squaring both sides
We get a² -2a/a +1/a² which is a² +1/a² -2=5×5
Which further is a²+1/a²-2=25—Eq2
Now adding 4 to both sides
a²+1/a²-2+4=25+4
Which is a²+2+1/a²=29
Further square root of both sides
√a²+2+1/a²=√29
a+1/a=√29
Now in problem the then asked what is a²-1/a² is (a+1/a)(a-1/a)
a+1/a ×a-1/a
Whereas in question a-1/a=5 and a+1/a=√2
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Les Foster
Answered 2 years ago
I have one problem with this … problem. It would be much more easily interpreted if there were parentheses. It looks like it could be either:
(a-1)/a = 5
or
a - (1/a) = 5
Very different problems. If it is the former, you can solve for ‘a’ as the other answer states. If it is the later, multiple all terms by ‘a’.
a^2 -1 = 5a
a^2 - 5a - 1 = 0
And at this point, use the quadratic formula to find the two possible values of ‘a’. From there, just plug those values into the other formula.
Still two things to consider:
the other formula may be ambiguous as well
sometimes things that pop out of quadratic may not
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Elaine Dawe
Answered 2 years agoDavid Vanderschel
a−1a=5
(a+1a)2=a2+2+1a2=a2−2+1a2+4=(a−1a)2+4=52+4=29
a+1a=±29−−√
a2−1a2=(a+1a)(a−1a)=±29−−√⋅5
a2−1a2=±529−−√
William Mccoy
Answered 6 years ago
First, solve for “a” in the first equation as follows:
(a‒ 1)/a = 5
a[(a‒ 1)/a] = 5(a)
On the left side of the above equation, cancelling out a factor of “a” in both the numerator and the denominator, we get:
(1)[(a‒ 1)]/1 = 5a
a‒ 1 = 5a
5a = a ‒ 1 since equality is symmetric, i.e., if a = b, then b = a.
5a + (‒a) = a ‒ 1 + (‒a)
5a + (‒a) = a + (‒1) + (‒a)
5a + (‒a) = [a + (‒a)] + (‒1)
4a = 0 + (‒1)
(1/4)4a = ‒1(1/4)
a = ‒1/4
Now, evaluating the rational expression (a²-1)/a² for a = ‒1/4 as follows:
(a² ‒ 1)/a² = [(‒1/4)² ‒ 1]/(‒1/4)²
= [(1/16) ‒ (16/16)]/(1/16)
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Step-by-step explanation:
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