Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
Advertisements
उत्तर
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
संबंधित प्रश्न
Solve the following quadratic equation for x : 4x2 − 4a2x + (a4 − b4) =0.
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.
The sum of the squares of three consecutive natural numbers as 149. Find the numbers
A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
Solve:
`1/p + 1/q + 1/x = 1/(x + p + q)`
`x^2-4x+1=0`
Two natural number differ by 3 and their product is 504. Find the numbers.
Find two consecutive multiples of 3 whose product is 648.
The values of k for which the quadratic equation \[16 x^2 + 4kx + 9 = 0\] has real and equal roots are
Solve the following equation: 3x2 + 25 x + 42 = 0
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.
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
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.
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
If car A use 4 litre of petrol more than car B in covering the 400 km, write down and equation in x and solve it to determine the number of litre of petrol used by car B for the journey.
Solve (x2 + 3x)2 - (x2 + 3x) -6 = 0.
Solve the following equation by factorization
`a/(ax - 1) + b/(bx - 1) = a + b, a + b ≠ 0, ab ≠ 0`
By selling an article for Rs. 21, a trader loses as much per cent as the cost price of the article. Find the cost price.
