Question

√5-1 √√5+1 =a+b√5, find a and b. √5+1 √√5-1​

Answer 1

Answer:

a=3 and b=0

Step-by-step explanation:

+5+15−1=a+b5

\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+b5

\frac{(\sqrt{5}+1)^2+(\sqrt{5}-1)^2}{5-1}=a+b\sqrt{5}5−1(5+1)2+(5−1)2=a+b5

\frac{5+1+2\sqrt{5}+5+1-2\sqrt{5}}{4}=a+b\sqrt{5}45+1+25+5+1−25=a+b5

\frac{12+0\sqrt{5}}{4}=a+b\sqrt{5}412+05=a+b5

3+0\sqrt{5}=a+b\sqrt{5}3+05=a+b5