Advertisements
Advertisements
Question
Solve the following by reducing them to quadratic equations:
`((7y - 1)/y)^2 - 3 ((7y - 1)/y) - 18 = 0, y ≠ 0`
Advertisements
Solution
The given equation
`((7y - 1)/y)^2 - 3 ((7y - 1)/y) - 18 = 0, y ≠ 0`
Putting `(7y - 1)/y`` = z`, then given equation becomes
z2 - 3z - 18 = 0
⇒ z2 - 6z + 3z - 18 = 0
⇒ z(z - 6) + 3(z - 6) = 0
⇒ (z - 6) (z + 3) = 0
⇒ z - 6 = 0 or z + 3 = 0
⇒ z = 6 or z = -3
But `(7y - 1)/y =z`
∴ `(7y - 1)/y` = 6
⇒ 7y - 1
= 6y
⇒ 7y - 6y
= 1
⇒ y = 1
Also `(7y - 1)/y`
= -3
⇒ 7y - 1
= -3y
⇒ 7y + 3y -1 = 0
⇒ 10y = 1
⇒ y = `(1)/(10)`
Hence, the required roots are `(1)/(10),1`.
RELATED QUESTIONS
The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples ?
The positive value of k for which the equation x2 + kx + 64 = 0 and x2 – 8x + k = 0 will both have real roots, is ______.
Solve the following equation: (x-8)(x+6) = 0
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Solve the following equation by factorization
`x/(x - 1) + (x - 1)/x = 2(1)/(2)`
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
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.
- If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.
A man spent Rs. 2800 on buying a number of plants priced at Rs x each. Because of the number involved, the supplier reduced the price of each plant by Rupee 1.The man finally paid Rs. 2730 and received 10 more plants. Find x.
Find the roots of the following quadratic equation by the factorisation method:
`3x^2 + 5sqrt(5)x - 10 = 0`
