Question
I. x2 – 7x + 12 = 0 II.
y2 – 7y + 10 = 0 In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.Solution
I. x2 – 7x + 12 = 0 => x2 – 4x – 3x + 12 = 0 => x(x – 4) – 3(x – 4) = 0 => (x – 4) (x – 3) = 0 => x = 4, 3 II. y2 – 7y + 10 = 0 => y2 – 5y – 2y + 10 = 0 => y(y – 5) – 2(y – 5) = 0 => (y – 5) (y – 2) = 0 => y = 5, 2 Hence, relation cannot be established. Alternate Method: if signs of quadratic equation is -ve and +ve respectively then the roots of equation will be +ve and +ve. So, roots of first equation = x = 4, 3 So, roots of second equation = y = 5, 2 After comparing we can conclude that relationship cannot be established between x and y.
A mixture contains milk and water in the ratio 7:8, respectively. If half of the mixture is replaced with 8 litres of water, then the resultant mixture ...
A jar contains a mixture of mango juice and water in the ratio of 5:2. 84 litres of the mixture was taken out and 34 litres of water was added to it. If...
In mixture 'X,' there are (4a + 20) liters of Juice and the remaining 20% consists of Soda.When mixture 'X' is combined with mixture 'Y,' which contains...
A 300 ml mixture consists of cow's milk and buffalo's milk. Cow's milk contains 10% fat, while buffalo's milk contains 15% fat. The total fat content in...
A 1000 ml mixture contains milk and water in the ratio of 7:3. 10% of the mixture is removed and some water is added so that the new ratio of milk to wa...
A milkman mixed milk and water in an empty container in the ratio 14:9. The quantity of milk mixed was bought by the milkman at the rate of Rs. 25/litre...
A mixture (milk + water + honey) contains ‘14m’ litres milk, ‘21n’ litres water and 49 litres more honey than water. If 25% of the mixture was r...
380 ml of a mixture contains milk and water in the ratio of 9 respectively. If 60 ml of water and 70 ml of milk are added into it, then the ratio of mil...
A container contains 720 litres of oil and kerosene mixed in the ratio 5:7. If ‘z’% of the total mixture is removed, and the amount of kerosene remo...
A Vessel if full of milk, 5 litre of milk is taken out and replaced by water. This process is repeated once more, find the initial amount of milk in the...
