Question
If x4 – 62x2 + 1 = 0, then a
value of x 3 + x -3 can be:Solution
x4 – 62x2 + 1 = 0 Divide by x2 x2 – 62 + 1/x2 = 0 ⇒ x2 + 1/x2 = 62 As we know, (x + 1/x)2 = x2 + 1/x2 + 2 ⇒ (x + 1/x)2 = 62 + 2 = 64 ⇒ x + 1/x = √64 = 8 Again, As we know, (x + 1/x)3 = x3 + 1/x3 + 3 (x + 1/x) ⇒ 83 = x3 + 1/x3 + 3 × 8 ⇒ x3 + 1/x3 = 512 – 24 = 488
Find the equation of the line passing through the point (3, 4) and having a slope of 2.
- A sum of Rs. 55,000 becomes Rs. 72,600 after 2 years when invested at simple interest at r% per annum. What will be the simple interest earned on Rs. 80,00...
P invested Rs. 7,000 at a simple interest rate of 22% per annum, while Q invested an unknown sum at a compound interest rate of 2...
If the sum of remainders, obtained on dividing 52436 by 22 and 59461 by 73, is divided by 13, then the remainder will be:
A person who spends 55% of his salary saves the remainder. His salary goes up by 15%, but his savings stay the same, and he now spends Rs. 3,300 more. D...
'O' is the incentre of △ABC. Given that ∠ABC = 64° and ∠BCA = 96°, determine the measure of ∠BOC.
Find the simplified value of the following expression:
(16.25 × 24 + 7 × √36) ÷ 23 + 3.75 × 16 – 37 × 2 + 7.5
...In the expansion of (1 + x)¹⁵ , what is the ratio of the coefficients of the 6th term to the 9th term?
If sin A + cos A = 1, what is the value of tan A?