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Correct explanation:
If 3+√7 / 3-√7 = a+b√7 find a and b.
Answer.:
We have been given that 3+√7/3-√7 = a+b√7.
We have been given that 3+√7/3-√7 = a+b√7.Inorder to rationalize this, we need yo multiply by 3+√7 in both numerator and denominator
=> (3+√7)² / (3-√7)(3+√7) = a + b√7
=> (3+√7)² / (3-√7)(3+√7) = a + b√7
=> (9 + 7 + 6√7) / (3² -√7²) = a + b√7
=> (3+√7)² / (3-√7)(3+√7) = a + b√7
=> (9 + 7 + 6√7) / (3² -√7²) = a + b√7
=>=> 16+ 6√7 / 9-7 = a + b√7
=> 16+ 6√7 / 9-7 = a + b√7=> 16+ 6√7 / 2 = a + b√7
=> 2(8 + 3√7) / 2 = a + b√7 [Taking 2 as common]
=> 8 +3√7 = a + b√7
Now, on comparing both sides,
we get a = 8 and b = 3.
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