Find the values of a and b if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = a+√5 b
Last updated at April 16, 2024 by Teachoo
Rationalising
Rationalising denominator of irrational number
Add (3√2+7√3) and (√2−5√3)
Divide 5√11 by 3√33
Multiply 2√15 by 7√5
Simplify (√5+√7)^2
Simplify (√4−√13)(√4+√13)
Simplify (9−√3)(9+√3)
Simplify (3√5−5√2)(4√5+3√2)
Rationalise the denominator of 8/√7
Rationalise the denominator of 1/((8 + 5√2))
Simplify (7√3)/(√10 + √3)−(2√5)/(√6 + √5)−(3√2)/(√15 + 3√2)
Multiple Choice Questions - Chapter 1 Class 9 Maths
Example 16
If a and b are rational numbers and (√11 − √7)/(√11 + √7) = a – b√77, find the value of a and b
Example 17
Find the values of a and b if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = a+√5 b You are here
Ex 1.4, 5 (i)
If x = 1/(2 − √3), find the value of x^3 − 2x^2 − 7x + 5
If a = 5 + 2√6 and b = 1/a, then what will be the value of a^2+b^2 ?
Example 18
Example 19 Important
Chapter 1 Class 9 Number Systems
Concept wise
- Rational numbers - Definition
- Finding rational number between two numbers
- Irrational Numbers
- Simplifying real numbers
-
Rationalising
- Laws of exponents
- Finding decimal expansion
- Expressing decimal in p/q
- Classifiying rational/irrational
- Finding irrational numbers b/w two numbers
- Real numbers on a number line
Transcript
Find the values of 𝑎 and 𝑏 if (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = 𝑎+√5 𝑏 We have (7 + 3√5)/(3 + √5) – (7 − 3√5)/(3 − √5) = ((7 + 3√5))/((3 + √5)) × ((3 − √5))/((3 − √5)) – ((7 − 3√5))/((3 − √5)) × ((3 + √5))/((3 + √5)) = (7(3 − √5) + 3√5(3 − √5))/((3 + √5) (3 − √5)) = ((21 − 7 √5 + 9 √5 − 15))/((3 + √5) (3 − √5)) – ((21 + 7 √5 − 9 √5 − 15))/((3 − √5) (3 + √5)) = ((6 + 2√5))/((9 − 5))−((6 − 2√5))/((9 − 5)) = (6 + 2√5)/4−((6 − 2√5))/4 = (6 + 2√5 − 6 + 2√5)/4 = (4√5)/4 = √5 Comparing with a + √5 b Hence, a = 0 and b = 1
