Advertisements
Advertisements
Question
Solve the following equations for the unknown: (6p + 9)2 + (8p - 7)2 = (10p + 3)2 - 71
Solution
(6p + 9)2 + (8p - 7)2 = (10p + 3)2 - 71
[36p2 + 81 + 2(6p)(9)] + [64p2 + 49 - 2(8p)(7)] = 100p2 + 9 + 2(10p)(3) - 71
⇒ 100p2 + 130 + 2 x 54p - 2 x 54p - 2 x 56p = 100p2 + 9 - 71 + 60p
Collecting like terms,
⇒ 130 + 71 - 9 = 60p + 4p
⇒ 192 = 64p
⇒ p = 3.
APPEARS IN
RELATED QUESTIONS
Solve the following equation:
`"p" - 12 = 2 2/3`
If 5 is subtracted from three times a number, the result is 16. Find the number.
Solve the following equation for the unknown: `(1)/(2)"p" + (3)/(4)"p"` = p - 3
Solve the following equations for the unknown: `2 + (3x - 2)/(3x + 2) = (3x + 2)/(x + 1)`
A number is as much greater than 21 as it is less than 71. Find the number.
If a motorcyclist drives at the rate of 24km/h, he reaches his destination 5 minutes too late. If he drives at the rate of 30 km/h, he reaches his destination 4minutes too soon. How far is his destination?
A police car is ordered to chase a speeding car which is 5 km ahead and is travelling at an average speed of 80 km/h. The police car is running at an average speed of 100 km/h. How long it take for the police car to overtake the speeding car?
In an isosceles triangle, each of the two equal sides is 4 cm more than the base. If the perimeter of the triangle is 29 cm, find the sides of the triangle.
A and B together can do a piece of work in 4 days, but A alone can do it in 12 days. How many days would B alone take to do the same piece of work?
A boy played 100 games, gaining Rs 50 on each game that he won, and losing Rs 20 for each game that he lost. If on the whole he gained Rs 800, find the number of games that he won.
