Advertisements
Advertisements
Question
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
Advertisements
Solution
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
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
Solve the following quadratic equations by factorization:
a2x2 - 3abx + 2b2 = 0
Solve the following quadratic equations by factorization:
`(x+3)/(x+2)=(3x-7)/(2x-3)`
`x^2+8x-2=0`
Find two consecutive multiples of 3 whose product is 648.
Solve for x: `3x^2-2sqrt3x+2=0`
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.
Solve the following equation:
(2x+3) (3x-7) = 0
Solve the following equation: 4x2 + 16x = 0
Solve the following equation: 2x2 - x - 6 = 0
Solve the following equation: `("a+b")^2 "x"^2 - 4 "abx" - ("a - b")^2 = 0`
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions 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.
The length of verandah is 3m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x, breadth of the verandah write an equation in ‘x’ that represents the above statement.
(ii) Solve the equation obtained in above and hence find the dimension of verandah.
In each of the following, determine whether the given values are solution of the given equation or not:
2x2 - x + 9 = x2 + 4x + 3; x = 2, x = 3
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈Q
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.
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
