Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
Advertisements
उत्तर
\[16x - \frac{10}{x} = 27\]
\[ \Rightarrow 16 x^2 - 10 = 27x\]
\[ \Rightarrow 16 x^2 - 27x - 10 = 0\]
\[ \Rightarrow 16 x^2 - 32x + 5x - 10 = 0\]
\[ \Rightarrow 16x\left( x - 2 \right) + 5\left( x - 2 \right) = 0\]
\[ \Rightarrow \left( 16x + 5 \right)\left( x - 2 \right) = 0\]
\[ \Rightarrow 16x + 5 = 0 \text { or } x - 2 = 0\]
\[ \Rightarrow x = - \frac{5}{16} \text { or } x = 2\]
Hence, the factors are 2 and \[- \frac{5}{16}\].
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
a2x2 - 3abx + 2b2 = 0
A two digit number is such that the product of the digits is 16. When 54 is subtracted from the number the digits are interchanged. Find the number
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
Solve each of the following equations by factorization:
`9/2x=5+x^2`
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Solve the following quadratic equations by factorization:
`x^2 – (a + b) x + ab = 0`
The sum of natural number and its reciprocal is `65/8` Find the number
Solve the following quadratic equations by factorization: \[\frac{1}{2a + b + 2x} = \frac{1}{2a} + \frac{1}{b} + \frac{1}{2x}\]
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
If the equation x2 + 4x + k = 0 has real and distinct roots, then
If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
Solve the following equation: a2x2 - 3abx + 2b2 = 0
Solve equation using factorisation method:
x(x – 5) = 24
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.
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
the return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Two years ago, a man’s age was three times the square of his daughter’s age. Three years hence, his age will be four times his daughter’s age. Find their present ages.
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
