Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
उत्तर
We have been given
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
`(x^2+a^2-2ax+x^2+b^2-2bx)/(x^2-(a+b)x+ab)=(a^2+b^2)/(ab)`
2abx2 - 2(ab)(a + b)x + ab(a2 + b2) = (a2 + b2)x2 - (a + b)(a2 + b2)x + ab(a2 + b2)
(a - b)2x2 - (a + b)(a - b)2x = 0
x(a - b)2(x - (a + b)) = 0
Therefore,
x(a - b)2 = 0
x = 0
or,
x - (a + b) = 0
x = a + b
Hence, x = 0 or x = a + b.
APPEARS IN
संबंधित प्रश्न
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
Solve each of the following equations by factorization:
`2x^2-1/2x=0`
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Find the value of k for which the following equations have real and equal roots:
\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]
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.
An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
Solve the quadratic equation by factorisation method:
x2 – 15x + 54 = 0
