Advertisements
Advertisements
Question
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
Advertisements
Solution
We have been given
a(x2 + 1) - x(a2 + 1) = 0
ax2 - (a2 + 1)x + a = 0
ax2 - a2x - x + a = 0
ax(x - a) - 1(x - a) = 0
(ax - 1)(x - a) = 0
Therefore,
ax - 1 = 0
ax = 1
x = 1/a
or,
x - a = 0
x = a
Hence, x = 1/a or x = a
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations
(i) 7x2 = 8 – 10x
(ii) 3(x2 – 4) = 5x
(iii) x(x + 1) + (x + 2) (x + 3) = 42
Find two consecutive positive integers, sum of whose squares is 365.
Solve the following quadratic equations by factorization:
(a + b)2x2 - 4abx - (a - b)2 = 0
Solve the following quadratic equations by factorization:
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4
Two squares have sides x cm and (x + 4) cm. The sum of this areas is 656 cm2. Find the sides of the squares.
An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.
Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
Solve:
x(x + 1) + (x + 2)(x + 3) = 42
`x^2+8x-2=0`
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Find k if x = 3 is a root of equation kx2 – 10x + 3 = 0.
Find the values of k for which the quadratic equation
\[\left( 3k + 1 \right) x^2 + 2\left( k + 1 \right)x + 1 = 0\] has equal roots. Also, find the roots.
Find the values of p for which the quadratic equation
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Solve the following equation: `"m"/"n" "x"^2 + "n"/"m" = 1- 2"x"`
Solve equation using factorisation method:
2(x2 – 6) = 3(x – 4)
Divide 29 into two parts so that the sum of the square of the parts is 425.
Solve the following equation by factorization
(x – 3) (2x + 5) = 0
Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.
