Advertisements
Advertisements
प्रश्न
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
Solve by completing the square:
x2 – 2ax + (a2 – b2) = 0
Advertisements
उत्तर
We have, x2 – 2ax + (a2 – b2) = 0
⇒ x2 – ((a + b) + (a – b))x + (a2 – b2) = 0
⇒ x2 – (a + b)x – (a – b)x + (a + b) (a – b) = 0 ...[∵ a2 – b2 = (a + b) (a – b)]
⇒ x(x – (a + b)) – (a – b) (x – (a + b)) = 0
⇒ (x – (a + b)) (x – (a – b) = 0
⇒ x = a + b, a – b
APPEARS IN
संबंधित प्रश्न
Solve for x :
`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`
Solve the following quadratic equations by factorization:
9x2 − 3x − 2 = 0
Solve the following quadratic equations by factorization:
abx2 + (b2 – ac)x – bc = 0
Solve the following quadratic equations by factorization:
`1/(x-1)-1/(x+5)=6/7` , x ≠ 1, -5
Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.
Two number differ by 4 and their product is 192. Find the numbers?
Solve:
`1/p + 1/q + 1/x = 1/(x + p + q)`
Solve for x: `3x^2-2sqrt3x+2=0`
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.
If the sum and product of the roots of the equation kx2 + 6x + 4k = 0 are real, then k =
Solve the following equation: a2x2 - 3abx + 2b2 = 0
Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
The outward journey
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
In each of the following, determine whether the given values are solution of the given equation or not:
`a^2x^2 - 3abx + 2b^2 = 0; x = a/b, x = b/a`.
Find three successive even natural numbers, the sum of whose squares is 308.
Paul is x years old and his father’s age is twice the square of Paul’s age. Ten years hence, the father’s age will be four times Paul’s age. Find their present ages.
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.
