Question

If x=(2+^5)^1/2 + (2-^5)^1/2 and y=(2+^5)^1/2 + (2-^5)^1/2 then evaluate x(square) + y (square)

Answer 1

5 is power of what term ??

Answer 2

can you please rewrite by using equation option?

Answer 3

ill write the question in equation form ...pls.. wait

Answer 4

\[if x=(2+\sqrt{5)}^{1/2} + (2-\sqrt{5})^{1/2}\]

Answer 5

\[and y=(2+\sqrt{5})^{1/2} - (2-\sqrt{5})^{1/2}\]

Answer 6

evaluate \[x ^{2}+y ^{2}\]

Answer 7

nw can u help me find the answer

Answer 8

note that xy = 2sqrt(5)
and x+y = 2* sqrt( 2+ _/5)
=>x^2 +y^2 = (x+y)^2 - 2xy
hope you can simplify further..

Answer 9

Does it help ??

\[\large x^2 + y^2 = (x+y)^2 - 2xy\]

Answer 10

nop

Answer 11

why not ?

Answer 12

i did nt understand

Answer 13

\[(x+y)^2 = [(2 + \sqrt{5})^{\frac{1}{2}} +(2 + \sqrt{5})^{\frac{1}{2}} + (2 + \sqrt{5})^{\frac{1}{2}} - (2 + \sqrt{5})^{\frac{1}{2}}]^2\]

\[(x+y)^2 = [2(2 + \sqrt{5})^{\frac{1}{2}}]^2 \implies (x+y)^2 = 4(2 + \sqrt{5})\]

Answer 14

\[((2+\sqrt{5})^{0.5}+(2-\sqrt{5})^{0.5})^{2}=(2+\sqrt{5})^{0.5\times2}+2(2+\sqrt{5})^{0.5}(2-\sqrt{5})^{0.5}+(2-\sqrt{5})^{2}\]

Answer 15

can you continue after it..?

Answer 16

\[xy = ((2 + \sqrt{5})^{\frac{1}{2}} + (2 + \sqrt{5})^{\frac{1}{2}})((2 + \sqrt{5})^{\frac{1}{2}} - (2 + \sqrt{5})^{\frac{1}{2}})\]

\[xy = (2 + \sqrt{5} - 2 + \sqrt{5}) \implies xy = 2 \sqrt{5}\]

Answer 17

\[x^2 + y^2 = 8 + 4\sqrt{5} - 4\sqrt{5} = ??\]

Answer 18

x=\[(2+\sqrt{5})^{1/2} + (2\sqrt{5})^{1/2}\]

Answer 19

sry.....nt that

Answer 20

\[x= (2+\sqrt{5})^{1/2} + (2-\sqrt{5})^{1/2} \]

Answer 21

See:

\[(x+y)^2 = [(2 + \sqrt{5})^{\frac{1}{2}} +(2 + \sqrt{5})^{\frac{1}{2}} + (2 + \sqrt{5})^{\frac{1}{2}} - (2 + \sqrt{5})^{\frac{1}{2}}]^2\]

\[(x+y)^2 = [2(2 + \sqrt{5})^{\frac{1}{2}}]^2 \implies (x+y)^2 = 4(2 + \sqrt{5})\]

Answer 22

This is your value for \((x+y)^2\)

Now find xy first:

\[xy = ((2 + \sqrt{5})^{\frac{1}{2}} + (2 + \sqrt{5})^{\frac{1}{2}})((2 + \sqrt{5})^{\frac{1}{2}} - (2 + \sqrt{5})^{\frac{1}{2}})\]

\[xy = (2 + \sqrt{5} - 2 + \sqrt{5}) \implies xy = 2 \sqrt{5}\]

So you have now both the values..

Answer 23

\[\large x^2 + y^2 = 8 + 4\sqrt{5} - 4\sqrt{5} = ??\]

Can you solve this now??