Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
4x2 + 4bx - (a2 - b2) = 0
Advertisements
उत्तर
4x2 + 4bx - (a2 - b2) = 0
4x2 + 2(a + b)x - 2(a - b)x - (a2 - b2) = 0
2x(2x + a + b) - (a - b)(2x + a + b) = 0
(2x - (a - b))(2x + a + b) = 0
Therefore,
2x - (a - b) = 0
2x = a - b
`x=(a-b)/2`
or,
2x + a + b = 0
2x = -(a + b)
`x=(-(a+b))/2`
Hence, `x=(a-b)/2` or `x=(-(a+b))/2`
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation for x : 4x2 − 4a2x + (a4 − b4) =0.
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?
Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
Solve the following quadratic equations by factorization:
`2(x^2 – 6) = 3 ( x – 4)`
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.
Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
The sum of a number and its reciprocal is `2 9/40`. Find the number.
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Solve the following equation by factorisation :
3x2 + 11x + 10 = 0
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
Solve the following quadratic equation by factorization method.
3p2 + 8p + 5 = 0
The polynomial equation x(x + 1) + 8 = (x + 2) (x – 2) is:
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
