Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
\[\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}; x \neq 3, 5\]
Advertisements
उत्तर
\[\frac{x - 2}{x - 3} + \frac{x - 4}{x - 5} = \frac{10}{3}\]
\[ \Rightarrow \frac{x - 2}{x - 3} - \frac{10}{3} = - \frac{x - 4}{x - 5}\]
\[ \Rightarrow \frac{3\left( x - 2 \right) - 10\left( x - 3 \right)}{3\left( x - 3 \right)} = - \frac{x - 4}{x - 5}\]
\[ \Rightarrow \frac{3x - 6 - 10x + 30}{3x - 9} = - \frac{x - 4}{x - 5}\]
\[ \Rightarrow - \frac{7x - 24}{3x - 9} = - \frac{x - 4}{x - 5}\]
\[ \Rightarrow \left( 7x - 24 \right)\left( x - 5 \right) = \left( 3x - 9 \right)\left( x - 4 \right)\]
\[ \Rightarrow 7 x^2 - 59x + 120 = 3 x^2 - 21x + 36\]
\[ \Rightarrow 4 x^2 - 38x + 84 = 0\]
\[ \Rightarrow 2 x^2 - 19x + 42 = 0\]
\[ \Rightarrow 2 x^2 - 12x - 7x + 42 = 0\]
\[ \Rightarrow 2x(x - 6) - 7(x - 6) = 0\]
\[ \Rightarrow (2x - 7)(x - 6) = 0\]
\[ \Rightarrow 2x - 7 = 0 \text { or } x - 6 = 0\]
\[ \Rightarrow x = \frac{7}{2} \text { or } x = 6\]
Hence, the factors are 6 and \[\frac{7}{2}\].
APPEARS IN
संबंधित प्रश्न
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?
The sum of two number a and b is 15, and the sum of their reciprocals `1/a` and `1/b` is 3/10. Find the numbers a and b.
Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]
Show that x = −3 is a solution of x2 + 6x + 9 = 0.
If the equation x2 + 4x + k = 0 has real and distinct roots, then
Solve the following equation : x2 + 2ab = (2a + b)x
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
Solve the following equation by factorization
x(2x + 5) = 3
Solve the following equation by factorization
`(1)/(7)(3x – 5)^2`= 28
Solve the following equation by factorization.
a2x2 + 2ax + 1 = 0, a ≠ 0
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
Solve the following equation by factorization
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2(1)/(2)`
If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm2. However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm2. Determine the sides of the two squares.
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
If the discriminant of the quadratic equation 3x2 - 2x + c = 0 is 16, then the value of c is ______.
4x2 – 9 = 0 implies x is equal to ______.
If `x + 1/x = 2.5`, the value of x is ______.
