Question

find the value of a and b if (5+3√2)÷(5-3√2)=a+b√2​

Answer 1

Given: (5 + 3√2) ÷ (5 - 3√2) = a + b√2​.

To find: The value of a and b.

Answer:

(5 + 3√2) ÷ (5 - 3√2)

Rationalizing the denominator,

(5 + 3√2)*(5 + 3√2)/(5 - 3√2)*(5 + 3√2)

= (5 + 3√2)^2/(5)^2 - (3√2)^2

= 25 + 30√2 + 18/25 - 18

= 43 + 30√2/7

∴ a = 43/7 and b = 30/7.

Answer 2

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