Question

If a=2-√5÷2+√5 and b=2+√5÷2-5, Find a²-b²
a) -144√5
b) 144 √5
c) 81√5
d) -81√5
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Answer 1

Answer:

Given,

a=[(2-√5)/(2+√5)] &

b=[(2+√5)/(2-√5)]

then

a²-b²=[(2-√5)/(2+√5)]² ×[(2+√5)/(2-√5)]²

Since we know that,

a²-b²= (a+b)(a-b)

therefore,

a²-b²

= [(2-√5)/(2+√5)+(2+√5)/(2-√5)]×[(2-√5)/. (2+√5)-(2+√5)/(2-√5)]

After simplification, we get

a²-b²= (-18)×(8√5)

a²-b²= -144√5 Ans.

therefore options (a) is right answer.