Question

if x=√5-2÷√5+2 and y=√5+2÷√5-2, find: xy​

Answer 1

Answer:

x = 7- 4√5 & y= 7+4√5

Step-by-step explanation:

x = (√5-2)/(√5+2)

multiplying numerator and denominator by (√5-2), we get,

x = (√5-2)(√5-2)/{(√5+2)(√5-2)}

x = (√5-2)(√5-2)/{(√5+2)(√5-2)}

x = (√5-2)²/{(√5)²-(2)²}

x= [(5+2+4√5)/(5-4)].

x = (√5-2)(√5-2)/{(√5+2)(√5-2)}

x = (√5-2)²/{(√5)²-(2)²}

x= [(5+2-4√5)/(5-4)]

x = 7- 4√5

y= (√5+2)/(√5-2)

multiplying numerator and denominator by (√5+2), we get,

y=(√5+2)²/[(√5-2)(√5+2)]

y= 5+2+4√5/{(√5)²-(2)²}

y= 7+4√5/ ( 5-4)

y= 7+4√5