Find a and b if4 + 3 root 5 upon 4 + 3 root 5 = a+ b root 5
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Answered by
1
Step-by-step explanation:
a=−
29
61
and a=-\frac{24}{29}a=−
29
24
Step-by-step explanation:
Given : \frac{4+3\sqrt{5}}{4-3\sqrt{5}}=a+b\sqrt{5}
4−3
5
4+3
5
=a+b
5
To find : The value of a and b?
Solution :
Taking LHS,
\frac{4+3\sqrt{5}}{4-3\sqrt{5}}
4−3
5
4+3
5
Rationalize the expression,
=\frac{4+3\sqrt{5}}{4-3\sqrt{5}}\times\frac{4+3\sqrt{5}}{4+3\sqrt{5}}=
4−3
5
4+3
5
×
4+3
5
4+3
5
=\frac{(4+3\sqrt{5})^2}{(4)^2-(3\sqrt{5})^2}=
(4)
2
−(3
5
)
2
(4+3
5
)
2
=\frac{16+45+24\sqrt5}{16-45}=
16−45
16+45+24
5
=\frac{61+24\sqrt5}{-29}=
−29
61+24
5
=\frac{61}{-29}+\frac{24\sqrt5}{-29}=
−29
61
+
−29
24
5
On comparing with RHS,
a=-\frac{61}{29}a=−
29
61
and a=-\frac{24}{29}a=−
29
24
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