Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7
Advertisements
उत्तर
We have been given
`1/(x+4)-1/(x-7)=11/30`
`(-11)/(x^2-3x-28)=11/30`
-30 = x2 - 3x - 28
x2 - 3x - 28 + 30 = 0
x2 - 3x + 2 = 0
x2 - 2x - x + 2 = 0
x(x - 2) - 1(x - 2) = 0
(x - 1)(x - 2) = 0
Therefore,
x - 1 = 0
x = 1
or,
x - 2 = 0
x = 2
Hence, x = 1 or x = 2.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
6x2 + 11x + 3 = 0
Two numbers differ by 3 and their product is 504. Find the number
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 separately, find the time in which each pipe would fill the tank separately.
Solve of the following equations, giving answer up to two decimal places.
3x2 – x – 7 =0
Solve : x2 – 11x – 12 =0; when x ∈ N
Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].
If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\] has equal roots, find the value of k.
If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax2 +bx + 1 = 0 having real roots is
The number of quadratic equations having real roots and which do not change by squaring their roots is
Solve the following equation: `"x"^2 - ( sqrt 2 + 1) "x" + sqrt 2 = 0 `
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.
There is a square field whose side is 44m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and graving the path at Rs 2. 75 and Rs. 1.5 per square metre, respectively, is Rs 4,904. Find the width of the gravel path.
Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.
In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`
Solve the following equation by factorization
`3x - (8)/x `= 2
Find the values of x if p + 1 =0 and x2 + px – 6 = 0
Find two consecutive odd integers such that the sum of their squares is 394.
A shopkeeper buys a certain number of books for Rs 960. If the cost per book was Rs 8 less, the number of books that could be bought for Rs 960 would be 4 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it to find the original cost of each book.
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
