Find x from the equation:(a+x+√a^2-x^2):(a+x-√a^2-x^2)=b:x
Answers
Given : (a+x+√a²-x²):(a+x-√a²-x²)=b:x
To find : x
Solution:
a+x+√a²-x² = √(a + x)² + √(a +x )(a - x) = √(a +x ) (√(a + x) + √(a -x ))
a+x-√a²-x² = √(a + x)² - √(a +x )(a - x) = √(a +x ) (√(a + x) - √(a -x )
(a+x+√a²-x²):(a+x-√a²-x²) = √(a +x ) (√(a + x) + √(a -x )) / √(a +x ) (√(a + x) - √(a -x )
=> (a+x+√a²-x²):(a+x-√a²-x²) = (√(a + x) + √(a -x )) / (√(a + x) - √(a -x )
Rationalizing
= (a + x + a - x + 2√(a + x)√(a -x )) / ( (a + x) - (a - x)
= (2a + 2√(a² - x²))/ 2x
= (a + √(a² - x²) / x
(a + √(a² - x²) / x = b/x
=> a + √(a² - x²) = b
=> √(a² - x²) = b - a
Squaring both sides
=> a² - x² = b² + a² - 2ab
=> - x² = b² - 2ab
=> x² = 2ab - b²
=> x = ±√( 2ab - b²)
Learn More:
rationalize the denominator of 4root3/5root5 and hence find their ...
brainly.in/question/17248397
(a) Rationalize the denominator: 14/ 5√3 − √5 Please Send ...
brainly.in/question/5471829