Question
If 3, x, y, 48 are in GP and x, y, 45 in AP, find x and
y.Solution
ATQ,
GP: x²=3y, y²=48x. AP: 2y = x + 45. From first: y= x²/3. Substitute → 2(x²/3) = x + 45 → 2x² = 3x + 135 → 2x²–3x–135=0. x= (3 ± √(9 + 1080))/4 = (3 ± 33)/4 → x=9 or –7.5. Take positive → x=9 → y=27. ✔ x = 9, y = 27.
I. x²= 961Â
II. y= √961
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 29x² - 137x + 108 = 0
Equation 2: 31y² - 146y + ...
I. 2p2 - 3p – 2 = 0 II. 2q2 - 11q + 15 = 0
I.√(3x-17)+ x=15
II. y + 135/y=24
Equation 1: x² - 200x + 9600 = 0
Equation 2: y² - 190y + 9025 = 0
I. 5x2 – 7x – 6 =0
II. 2y2 – 5y – 7 =0
I. 35x² - 24x – 35 = 0
II. 72y² - 145y + 72 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 40x + 375 = 0
Equation 2: y² - 36y + 324 = 0
What is the speed of the stream if a ship takes 15 hours to travel 240 km in calm waters, given that the ratio of its speed against the current to its s...
I. 7x² + 27x + 18 = 0
II. 19y² - 27y + 8 = 0
