Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
a2b2x2 + b2x - a2x - 1 = 0
Advertisements
उत्तर
We have been given
a2b2x2 + b2x - a2x - 1 = 0
b2x(a2x + 1) - 1(a2x + 1) = 0
(b2x - 1)(a2x + 1) = 0
Therefore,
b2x - 1 = 0
b2x = 1
`x=1/b^2`
or,
a2x + 1 = 0
a2x = -1
`x=-1/a^2`
Hence, `x=1/b^2` or `x=-1/a^2`
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
6x2 - x - 2 = 0
Solve the following quadratic equations by factorization:
`10x-1/x=3`
Solve the following quadratic equations by factorization:
`x^2-(sqrt3+1)x+sqrt3=0`
A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
Solve of the following equations, giving answer up to two decimal places.
3x2 – x – 7 =0
Solve the following quadratic equations by factorization:
(x + 1) (2x + 8) = (x+7) (x+3)
The sum of two natural numbers is 20 while their difference is 4. Find the numbers.
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.
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
Solve the following equation: (x-8)(x+6) = 0
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm2, find the hypotenuse.
Solve equation using factorisation method:
(2x – 3)2 = 49
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
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Find two consecutive natural numbers such that the sum of their squares is 61.
The product of two successive integral multiples of 5 is 300. Then the numbers are:
