Advertisements
Advertisements
प्रश्न
Solve `4x^2+4bx-(a^2-b^2)=0`
उत्तर
`4x^2+4bx-(a^2-b^2)=0`
⇒ `4x^2+4bx-(a-b)(a+b)=0`
⇒`4x^2+2[(a+b)-(a-b)]x-(a-b)(a+b)=0`
⇒`4x^2+2(a+b)x-2(a-b)x-(a-b)(a+b)=0`
⇒`2x[2x+(a+b)]-(a-b)[2x+(a+b)]=0`
⇒`[2x+(a+b)][2x-(a-b)]=0`
⇒`2x+(a+b)=0 or 2x-(a-b)=0`
⇒` x=(-a+b)/2` or ` x=(a-b)/2`
Hence, `-(a+b)/2` and `(a-b)/2` are the roots of the given equation.
APPEARS IN
संबंधित प्रश्न
A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train
Which of the following is a quadratic equation?
(a)` (x^2+1)=(2-x)^2+3` (b)` x^3-x^2=(x-1)^3`
(c) `2x^+3=(5+x)(2x-3)` (d) None of these
The length of a rectangular field exceeds its breadth by 8 m and the area of the field is `240 m^2` . The breadth of the field is
(a) 20 m (b) 30 m (c) 12 m (d) 16 m
Find the value of k so that the quadratic equation` x^2-4kx+k=0`
has equal roots.
The total cost of a certain length of a piece of cloth is Rs 200. If the piece was 5 m longer and each metre of cloth costs Rs 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre ?
Pratik takes 8 hours to travel 36 km downstream and return to the same spot. The speed of boat in still water is 12 km. per hour. Find the speed of water current.
Solve the following quadratic equation.
\[x^2 - \frac{3x}{10} - \frac{1}{10} = 0\]
A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water.
Mukund has ₹ 50 more than Sagar. If the product of the amount they have is 15,000, then find the amount each has
Present age of mother of Manish is 1 year more than 5 times the present age of Manish. Four years before, if the product of their ages was 22, then find the present age of Manish and his mother
