Advertisements
Advertisements
Question
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
Advertisements
Solution
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
Put `(x - 3)/(x + 3) = a,`
then `(x + 3)/(x - 3) = (1)/a`
∴ `a + (1)/a = (5)/(2)`
2a2 + 2 = 5a
⇒ 2a2 - 5a + 2 = 0
⇒ 2a2 - a - 4a + 2 = 0
⇒ a(2a - 1) -2(2a - 1) = 0
⇒ (2a - 1) (a - 2) = 0
Either 2a - 1 = 0,
then a = `(1)/(2)`
or
a - 2 = 0,
then a = 2
(a) When a = `(1)/(2)`, then
`(x - 3)/(x + 3) = (1)/(2)`
⇒ 2x - 6 = x + 3
⇒ 2x - x = 3 + 6
⇒ x = 9
(b) when a = 2, then
`(x - 3)/(x + 3) = (2)/(1)`
2x + 6 = x - 3
⇒ 2x - x = -3 - 6
⇒ x = -9
∴ x = 9, -9.
APPEARS IN
RELATED QUESTIONS
The hypotenuse of a right triangle is `3sqrt10` cm. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5` cm. How long are the legs of the triangle?
Sum of the areas of two squares is 640 m2. If the difference of their perimeters is 64 m. Find the sides of the two squares.
`8x^2-14x-15=0`
The sum of a natural number and its positive square root is 132. Find the number.
Find the two consecutive positive even integers whose product is 288.
Write the set of values of k for which the quadratic equation has 2x2 + kx – 8 = 0 has real roots.
Solve the following equation: `1/("x" - 1) + 2/("x" - 1) = 6/"x" , (x ≠ 0)`
Solve the following equation by factorization
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.
If the area of a square is 400 m2, then find the side of the square by the method of factorization.
