Express this with rational denominator b2/root of (a2+b2)+a
Source: RD Sharma Class 9 Ex 3.2 Q3 Part 9
Answers
Given : b²/(√(a² + b²) + a )
To find : Rationalize
Solution:
b²/(√(a² + b²) + a )
multiply numerator & denominator with (√(a² + b²) - a )
= b² x (√(a² + b²) - a ) / (√(a² + b²) + a ) x (√(a² + b²) - a )
using (x + y)(x - y) = x² - y²
x = √(a² + b²)
y = a
=> x² = a² + b²
y² = a²
=> x² - y² = a² + b² - a² = b²
Substituting these values in denominator
= b² x (√(a² + b²) - a ) / b²
= (√(a² + b²) - a )
= √(a² + b²) - a
b²/(√(a² + b²) + a ) = √(a² + b²) - a
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Answer:
b²/(√(a² + b²) + a )
multiply numerator & denominator with (√(a² + b²) - a )
= b² x (√(a² + b²) - a ) / (√(a² + b²) + a ) x (√(a² + b²) - a )
using (x + y)(x - y) = x² - y²
x = √(a² + b²)
y = a
=> x² = a² + b²
y² = a²
=> x² - y² = a² + b² - a² = b²
= b² x (√(a² + b²) - a ) / b²
= (√(a² + b²) - a )
= √(a² + b²) - a
b²/(√(a² + b²) + a ) = √(a² + b²) - a
Step-by-step explanation: