Question

If x= root 5+1/root5-1 and y=root5-1/root5+1, find x^2+y^2+xy

Answer 1

Answer:

See attachments.

Step-by-step explanation:

Because your note is not clear, there are two scenarios:

1). If  x = root(5+1) / root(5-1) and

y = root(5-1) / root(5+1) ,

then answer is 3$\frac{1}{6}$

2). If  x = [(root5) + 1] / [(root5) - 1]  and

y = [(root5) - 1] / [(root5) + 1] ,

then answer is 8 .

Answer 2

Answer:

x^2+y^2+xy

=(√5+1/√5-1)^2 + (√5-1/√5+1)^2 +

(√5+1/√5-1)(√5-1/√5+1)

={(√5+1)^2}/{(√5-1)^2} + {(√5-1)^2}/{(√5+1)^2} + (1)

={5+1+2√5}/{5+1-2√5} +{5+1-2√5}/{5+1+2√5} + (1)

={6+2√5}/{6-2√5} +{6-2√5}/{6+2√5} + (1)

(adding 1st two terms)

=[{6+2√5}^2+{6-2√5}^2]/[{6-2√5}×{6+2√5}] +(1)

=[{6^2+(2√5)^2+(2×6×2√5)+

6^2+(2√5)^2-(2×6×2√5)}]/[6^2-(2√5)^2] +(1)

=[6^2+(2√5)^2+6^2+(2√5)^2]/[36-20] +(1)

=[36+20+36+20]/[16] +(1)

=[112]/[16] +1

=[ 7 ] + [1]

= 8

(please mark as brainliest answer)