Advertisements
Advertisements
Question
Solve the following quadratic equations by factorization:
\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11; x \neq \frac{3}{5}, - \frac{1}{7}\]
Advertisements
Solution
\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11\]
\[ \Rightarrow \frac{3(7x + 1 )^2 - 4 \left( 5x - 3 \right)^2}{\left( 5x - 3 \right)\left( 7x + 1 \right)} = 11\]
\[ \Rightarrow \frac{3\left( 49 x^2 + 1 + 14x \right) - 4\left( 25 x^2 + 9 - 30x \right)}{35 x^2 + 5x - 21x - 3} = 11\]
\[ \Rightarrow \frac{147 x^2 + 3 + 42x - 100 x^2 - 36 + 120x}{35 x^2 - 16x - 3} = 11\]
\[ \Rightarrow 47 x^2 + 162x - 33 = 11\left( 35 x^2 - 16x - 3 \right)\]
\[ \Rightarrow 47 x^2 + 162x - 33 = 385 x^2 - 176x - 33\]
\[ \Rightarrow 385 x^2 - 47 x^2 - 176x - 162x - 33 + 33 = 0\]
\[ \Rightarrow 338 x^2 - 338x = 0\]
\[ \Rightarrow x^2 - x = 0\]
\[ \Rightarrow x\left( x - 1 \right) = 0\]
\[ \Rightarrow x = 0 \text { or } x - 1 = 0\]
\[ \Rightarrow x = 0 \text { or } x = 1\]
Hence, the factors are 0 and 1.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
(x − 4) (x + 2) = 0
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
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 the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.
In a two digit number, the unit’s digit is twice the ten’s digit. If 27 is added to the number, the digit interchange their places. Find the number.
Solve the equation 3x² – x – 7 = 0 and give your answer correct to two decimal places.
By increasing the speed of a car by 10 km/hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.
Solve the following quadratic equation by factorisation:
x2 - 3x - 10 = 0
Solve the following equation by factorization
`(1)/(x - 3) - (1)/(x + 5) = (1)/(6)`
Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )2 + 6(3x + 1) – 8 = 0
The length (in cm) of the hypotenuse of a right-angled triangle exceeds the length of one side by 2 cm and exceeds twice the length of another side by 1 cm. Find the length of each side. Also, find the perimeter and the area of the triangle.
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.
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
The product of two integers is –18; the integers are ______.
