Question
If a, b, c are in geometric progression and a + b + c =
14, a² + b² + c² = 84, find a, b, c.Solution
ATQ,
Let a = x, b = xr, c = xr² Sum: x(1 + r + r²) = 14 Squares: x²(1 + r² + r⁴) = 84 Divide 2nd by (1st)²: (1 + r² + r⁴)/(1 + r + r²)² = 84/14² = 84/196 = 3/7 Try r = 2 → (1+4+16)/(1+2+4)² = 21/49 = 3/7 ✅ Then x(7) =14 ⇒ x = 2 → (a,b,c) = (2,4,8)
Find the surface area of the smallest cube that can perfectly fit a sphere of volume 7776π cm3 inside it.
The surface area of water in a swimming pool forms a rectangle with length 30m and breadth 12m. The depth of water increases uniformly from 1.4m to 2.6m...
The circumference of a circle is 88 cm and the length of the rectangle is 4 times the radius of the circle. Find the area (in cm2) of the rec...
A cuboid has length 16 cm, breadth 12 cm and height 8 cm. If each dimension is increased by 25%, then what will be the new volume of the cuboid?
Determine the base length of an isosceles triangle with an area of 288 cm² and an altitude measuring 36 cm.
The diameter of the base of a cylindrical drum is 28 cm and its height is 15 cm. The drum is full of water and the water from the drum is transferred to...
The length of a cuboid increases by 5%, its breadth decreases by 10% and its height increases by 25%. Find the percentage change in the volume.
The sum of the areas of two circles P and Q is 20020 cm2. If the product of the diameters of both circles P and Q is 12348 cm, then find out ...
The sum of the area of rectangle A and B is 2964 cm 2 . The ratio between the breadth of rectangle A and length of rectangle B is 2:3 respect...
If the volume and radius of a cylinder is 13860 cm3 and 21 cm respectively then find the height of the cylinder?
