Question
If (x² + 1)/x = 3, what is the value of (x¹² + 1)/x
⁶ ?Solution
Given, (x² + 1)/x = 3 ⇒ (x + 1/x) = 3 ⇒ (x + 1/x)² = 3² [Squaring on both sides] ⇒ x² + 1/x² + 2 = 9 ⇒ x² + 1/x² = 7 ⇒ (x² + 1/x²)³ = 7³ [Cubing on both sides] ⇒ (x²)³ + (1/x²)³ + 3 .x² . 1/x² (x² + 1/x²) = 343 ⇒ x ⁶ + 1/x ⁶ + 3 (x² + 1/x²) = 343 ⇒ x ⁶ + 1/x ⁶ + 3 * 7 = 343 ⇒ x ⁶ + 1/x ⁶ = 322 ⇒ (x¹² + 1)/x ⁶ = 322
If the ratio of height and base of a parallelogram is 8:5, respectively and its area is 640 cm2, then find the difference between height and base of the...
The circumference of a circle is 55 cm and the length of the rectangle is 8 times the radius of the circle. Find the area (in cm2) of the rec...
A field is in the shape of a trapezium, where the distance between the two parallel sides is 60 metres. One of the parallel sides measures 30 metres, an...
The base of a triangle is 18 cm and height is 15 cm. The height of another triangle of double the area having the base 27 cm is:
A well with 42 m inside diameter is dug 14 m deep. Soil taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. F...
The area of four walls of a room is 144 cm2. If the length and breadth of the room were equal and the height of the room is 4 cm, then what i...
In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm then what is BD : BC ?
If the area of a triangle is 864 cm2 and base: corresponding altitude is 3:4, then the altitude of the triangle is:
Pankaj gives 15% of her salary to his wife, 5% of the remaining amount to his children and 20% of the remaining to his parents. If Pankaj is left with R...
ABCD is a cyclic quadrilateral, such that ratio of measures ∠A, ∠B and ∠C is 1 : 4 : 5, then the measure of ∠D is.
Relevant for Exams:
