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