Question

5 + 1 √5 - 1 9. If a = and b = √5 - 1 √5 + 1 find the value of (Va + b )2.​

Answer 1

Step-by-step explanation:

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