simplify 7+3√5/3+√5 - 7-3√5/3-√5 = a+ √5b
Answers
Answered by
1
a = 0 \: and \: b = 1
Step-by-step explanation:
LHS=\frac{7+3\sqrt{5}}{3+\sqrt{5}}-\frac{7-3\sqrt{5}}{3-\sqrt{5}}=\frac{(7+3\sqrt{5})(3-\sqrt{5})-(7-3\sqrt{5})(3+\sqrt{5})}{(3+\sqrt{5})(3-\sqrt{5})}=\frac{21-7\sqrt{5}+9\sqrt{5}-15-(21+7\sqrt{5}-9\sqrt{5}-15)}{3^{2}-(\sqrt{5})^{2}}
=\frac{21-7\sqrt{5}+9\sqrt{5}-15-21-7\sqrt{5}+9\sqrt{5}+15)}{9-5}
=\frac{4\sqrt{5}}{4}
=\sqrt{5}---(1)
RHS = a+\sqrt{5}b--(2)
Now\\0+\sqrt{5}=a+\sqrt{5}\\from\:(1)\:and\:(2)
a = 0 \: and \: b = 1
Therefore,
a = 0 \: and \: b = 1
•••♪
Answered by
1
Answer:
I think a is 0 and b is 1
please follow me
Similar questions