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a = 2 + √3 1/a = 1/(2 + √3) = 2 - √3 a + 1/a = 2 + √3 + 2 - √3 a + 1/a = 4 (a^6+a^4+a^2+1)/a^3 → (a^3 (a^3+a+1/a+1/a^3 ))/a^3 = a^3+a+1/a+1/a^3 = (a^3+1/a^3 ) + (a+1/a) a+1/a = 4 On cubing both sides, (a+1/a)^3 = (4)^3 a^3+1/a^3 + 3 × a×1/a (4) = 64 a^3+1/a^3 + 12 = 64 a^3+1/a^3 = 52 Therefore, a^3+1/a^3 + a+1/a = 52 + 4 = 56.
The ratio of a closed cuboid's length, width, and height is 5: 4: 3. The total surface area of this cuboid is 1500 cm². Find the volume (in cm³) of th...
The length, breadth and height of a solid cuboidal box are in the ratio 7 : 5 : 3 and its total surface area is 11502cm2. Its breadth is:
Number p is 15% more than 150. If k is 15% less than p, then k is equal to:
A circular clock has the hour hand of length 6 inch. Find the length of the distance it covers by it's tip from 9 p.m. to 3 a.m.
The inner radius of a cylindrical pipe is 7 cm. Water flows from this pipe at a speed of 5 km/h and falls into a rectangular tank 100 meters long and 44...
Angle bisectors of Q and R meet at point S, inside the triangle PQR. If angle QSR = 126˚ , then the measure of angle P is:
A man spends 70% of his income. If his income is increased by 25% and expenditure is increase by 20%. Find the % change in saving?
A circle has a radius of 21 cm and the area of its sector is 308 cm². Find the angle subtended by the arc at the center of the circle. (Use π = 22/7)<...
If the side of square and its area is in the ratio of 7:28 then find its perimeter?
Determine the volume (in cubic centimeters) of a cuboid whose adjacent face areas measure 320 cm², 480 cm², and 216 cm², respectively.
