Advertisements
Advertisements
प्रश्न
If x = `"pab"/("a + b")`, then prove that `("x + pa")/("x - pa") + ("x + pb")/("x - pb") = (2("a"^2 - "b"^2))/"ab"`
Advertisements
उत्तर
x = `"pab"/("a + b") => "x"/"pa" = "b"/("a + b")`
Applying componendo and dividendo
`("x + pa")/("x - pa") = ("b + a + b")/("b - a - b") = ("2b + a")/"- a"` .............(i)
Again , x = `"pab"/("a + b") => "x"/"pb" = "a"/("a + b")`
Applying componendo and dividendo
`("x + pb")/("x - pb") = ("a + a + b")/("a - a - b") = ("2a + b")/"- b"` .............(ii)
Adding (i) and (ii)
`("x + pa")/("x - pa") + ("x + pb")/("x - pb") = ("2b + a")/"- a" +("2a + b")/"- b" = ("a - 2"b"")/"a" + ("b - 2a")/"b"`
`= (-2"b"^2 + "ab" - 2"a"^2 + "ab")/"ab"`
`= (-2"b"^2 + 2 "ab" - 2"a"^2)/"ab"`
`= (2 ("a"^2 - "b"^2))/"ab"` = 2 = RHS
LHS = RHS
Hence proved.
APPEARS IN
संबंधित प्रश्न
A school has 630 students. The ratio of the number of boys to the number of girls is 3 : 2. This ratio changes to 7 : 5 after the admission of 90 new students. Find the number of newly admitted boys.
If r2 = pq, show that p : q is the duplicate ratio of (p + r) : (q + r).
Two positive numbers are in the ratio 3 : 5 and the difference between their squares is 400. Find the numbers.
Express the given ratio in its simplest form: 200 m : 5 km
A school collected Rs 2100 for charity. It was decided to divide the money between an orphanage and a blind school in the ratio of 3 : 4. How much money did each receive?
Write the following ratio in the simplest form:
1 L 35 mL : 270 mL
The ratio of the number of male and female workers in a textile mill is 5 : 3. If there are 115 male workers, what is the number of female workers in the mill?
Choose the correct answer from the given options :
A ratio equivalent to the ratio `(2)/(3) : (5)/(7)` is
Find the simplified form of the following ratio.
12 : 27
Divide 20 pens between Sheela and Sangeeta in the ratio of 3 : 2.
