Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
Advertisements
उत्तर
\[16x - \frac{10}{x} = 27\]
\[ \Rightarrow 16 x^2 - 10 = 27x\]
\[ \Rightarrow 16 x^2 - 27x - 10 = 0\]
\[ \Rightarrow 16 x^2 - 32x + 5x - 10 = 0\]
\[ \Rightarrow 16x\left( x - 2 \right) + 5\left( x - 2 \right) = 0\]
\[ \Rightarrow \left( 16x + 5 \right)\left( x - 2 \right) = 0\]
\[ \Rightarrow 16x + 5 = 0 \text { or } x - 2 = 0\]
\[ \Rightarrow x = - \frac{5}{16} \text { or } x = 2\]
Hence, the factors are 2 and \[- \frac{5}{16}\].
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation by factorization method : `3x^2-29x+40=0`
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples ?
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
Solve the following quadratic equations by factorization:
\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11; x \neq \frac{3}{5}, - \frac{1}{7}\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 + px + 3 = 0\]
Write the number of real roots of the equation x2 + 3 |x| + 2 = 0.
Solve the following equation: `("x" + 3)/("x" + 2) = (3"x" - 7)/(2"x" - 3)`
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
Find two consecutive positive even integers whose squares have the sum 340.
A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/hr more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.
In each of the following determine whether the given values are solutions of the equation or not.
3x2 - 2x - 1 = 0; x = 1
Solve the following equation by factorization
x2– 4x – 12 = 0,when x∈N
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
If the product of two positive consecutive even integers is 288, find the integers.
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, find the time in which each pipe would/fill the tank.
Solve the following equation by factorisation :
2x2 + ax – a2= 0
