if 3+root 7 divided 3-root 7 = a+b root 7 find the value of a and b
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Answers
Answered by
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Heya !!
3 + √7 / 3 - √7 = a + b√7
LHS = ( 3 + √7 ) / ( 3 - √7 )
Rationalizing the denominator ( 3 - √7).
=> ( 3 + √7 ) / ( 3 - √7 ) × ( 3 + √7 ) / ( 3+√7)
=> ( 3 + √7 ) ( 3 + √7 ) / ( 3 + √7)(3-√7)
=> ( 3 + √7)² / ( 3)² - (√7)²
=> (3)² + (√7)² + 2 × 3 × √7 / 9 - 7
=> 9 + 7 + 6√7 / 2
=> 16 + 6√7 / 2
=> 2 ( 8 + 3√7 ) / 2
=> 8 + 3√7.
Now,
LHS = RHS
8 + 3√7 = a + b√7.
Clearly,
a = 8 and b = 3.
3 + √7 / 3 - √7 = a + b√7
LHS = ( 3 + √7 ) / ( 3 - √7 )
Rationalizing the denominator ( 3 - √7).
=> ( 3 + √7 ) / ( 3 - √7 ) × ( 3 + √7 ) / ( 3+√7)
=> ( 3 + √7 ) ( 3 + √7 ) / ( 3 + √7)(3-√7)
=> ( 3 + √7)² / ( 3)² - (√7)²
=> (3)² + (√7)² + 2 × 3 × √7 / 9 - 7
=> 9 + 7 + 6√7 / 2
=> 16 + 6√7 / 2
=> 2 ( 8 + 3√7 ) / 2
=> 8 + 3√7.
Now,
LHS = RHS
8 + 3√7 = a + b√7.
Clearly,
a = 8 and b = 3.
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Answered by
4
3 and 8 are the value of a and b
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