find the value of a and b if √5-1/√5+1-√5+1/√5-1= a+ b√5
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Step-by-step explanation:
Step-by-step explanation:
\frac{\sqrt{5}+1}{\sqrt{5}-1}+\frac{\sqrt{5}-1}{\sqrt{5}+1}=a+b\sqrt{5}
5
−1
5
+1
+
5
+1
5
−1
=a+b
5
\frac{(\sqrt{5}+1)^2+(\sqrt{5}-1)^2}{(\sqrt{5}-1)(\sqrt{5}+1)}=a+b\sqrt{5}
(
5
−1)(
5
+1)
(
5
+1)
2
+(
5
−1)
2
=a+b
5
\frac{(\sqrt{5}+1)^2+(\sqrt{5}-1)^2}{5-1}=a+b\sqrt{5}
5−1
(
5
+1)
2
+(
5
−1)
2
=a+b
5
\frac{5+1+2\sqrt{5}+5+1-2\sqrt{5}}{4}=a+b\sqrt{5}
4
5+1+2
5
+5+1−2
5
=a+b
5
\frac{12+0\sqrt{5}}{4}=a+b\sqrt{5}
4
12+0
5
=a+b
5
3+0\sqrt{5}=a+b\sqrt{5}3+0
5
=a+b
5
comparing both sides we get
a=3 and b=0
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