a/1+1/a =1 find a*17+1/a*17
Answers
Step-by-step explanation:
a - \frac{1}{a} = \frac{15}{4}a−
a
1
=
4
15
Solution:
Given that,
a+\frac{1}{a} = \frac{17}{4}a+
a
1
=
4
17
To find: a - \frac{1}{a}a−
a
1
From given,
\begin{gathered}a+\frac{1}{a} = \frac{17}{4}\\\\Take\ square\ on\ both\ sides\\\\(a+\frac{1}{a})^2 = (\frac{17}{4})^2\\\\Expanding\\\\a^2 + \frac{1}{a^2}+ 2 = \frac{289}{16}\\\\a^2 + \frac{1}{a^2} = \frac{289}{16}-2\\\\a^2 + \frac{1}{a^2} = \frac{289-32}{16}\\\\a^2 + \frac{1}{a^2} = \frac{257}{16} ------ eqn 1\end{gathered}
a+
a
1
=
4
17
Take square on both sides
(a+
a
1
)
2
=(
4
17
)
2
Expanding
a
2
+
a
2
1
+2=
16
289
a
2
+
a
2
1
=
16
289
−2
a
2
+
a
2
1
=
16
289−32
a
2
+
a
2
1
=
16
257
−−−−−−eqn1
Now expand,
\begin{gathered}a - \frac{1}{a}\\\\Take\ square\\\\(a-\frac{1}{a})^2 = a^2 + \frac{1}{a^2} - 2\\\\Substitute\ eqn\ 1\\\\(a-\frac{1}{a})^2 = \frac{257}{16} - 2\\\\(a-\frac{1}{a})^2 = \frac{257 - 32}{16}\\\\(a-\frac{1}{a})^2 = \frac{225}{16}\\\\Take\ square\ root\ on\ both\ sides\\\\a - \frac{1}{a} = \frac{15}{4}\end{gathered}
a−
a
1
Take square
(a−
a
1
)
2
=a
2
+
a
2
1
−2
Substitute eqn 1
(a−
a
1
)
2
=
16
257
−2
(a−
a
1
)
2
=
16
257−32
(a−
a
1
)
2
=
16
225
Take square root on both sides
a−
a
1
=
4
15
Thus the required is found
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