if a and b are the rational no.s 3+√5÷3-√5=a+b×√5,find the values of a and b(with steps)
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plz go through the answer in the given photo
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aadeshyadav7:
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Hiii friend,
3+✓5/3-✓5
Rationalizing the Denominator 3-✓5
=> 3+✓5/3-✓5 × 3+✓5/3+✓5
=> (3+✓5)(3+✓5)/(3-✓5)(3+✓5)
=> (3+✓5)²/(3)² - (✓5)²
=> (3)² + (✓5)² + 2 × 3 × ✓5/9-5
=> 9 + 5 + 6✓5/4
=> 14+6✓5/4
=> 2(7+3✓5)/4
=> 7+3✓5/2 => 7/2 + 3✓5/2
Now,
LHS = RHS
7/2 + 3✓5/2 = A+B✓5
Clearly,
A = 7/2 and B = 3/2
HOPE IT WILL HELP YOU....... :-)
3+✓5/3-✓5
Rationalizing the Denominator 3-✓5
=> 3+✓5/3-✓5 × 3+✓5/3+✓5
=> (3+✓5)(3+✓5)/(3-✓5)(3+✓5)
=> (3+✓5)²/(3)² - (✓5)²
=> (3)² + (✓5)² + 2 × 3 × ✓5/9-5
=> 9 + 5 + 6✓5/4
=> 14+6✓5/4
=> 2(7+3✓5)/4
=> 7+3✓5/2 => 7/2 + 3✓5/2
Now,
LHS = RHS
7/2 + 3✓5/2 = A+B✓5
Clearly,
A = 7/2 and B = 3/2
HOPE IT WILL HELP YOU....... :-)
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