Question

find x and y if (√5-2)/(√5+2)=x +y√5
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Answer 1

Given :-

• (√5-2)/(√5+2)=x +y√5

To Find :-

• The value of x and y

Concept used :-

• Rationalisation.

Now,

→ (√5-2)/(√5+2)=x +y√5

→ √5 - 2/ √5 + 2 × √5 - 2 / √5 - 2 = x + y√5

→ (√5 - 2)²/ (√5)² - ( 2)² = x + y√5

→ (5 - 4√5 + 4 )/( 5 - 4) = x + y√5

→ 9 - 4√5 = x + y√5

→ 9 = x , -4√5 = y√5

→ x = 9, y = -4

Hence, The value of x and y is 9 & -4 respectively.