Exams › SSC CGL (Prelims) › General

If x + 1/x = -2, find the value of x^8 + 1/x^8 + 2x^5 + 2/x^5 + x^2 + 1/x^2.

1. 0
2. 2
3. -2
4. 4

Correct answer: 0

Solution

The equation x + 1/x = -2 has the unique solution x = -1 (since (x+1)^2 = 0). Substituting x = -1: x^8 + 1/x^8 = 1+1 = 2; 2x^5 + 2/x^5 = -2-2 = -4; x^2 + 1/x^2 = 1+1 = 2. The total is 2 - 4 + 2 = 0.

Related SSC CGL (Prelims) General questions

• A shopkeeper sells rice at a discount of 6% on the marked price but uses a weight that is 25% less than the actual weight. Find his overall profit percentage.
• The profit made on an article sold for ₹2400 is equal to the loss incurred when it is sold for ₹2000. What will be the profit or loss percentage if the article is sold for ₹2200?
• Train A leaves Station X at 5:00 AM at 50 km/h. Train B leaves Station Y at 7:30 AM at 80 km/h. Both trains move towards each other. The distance between the stations is 500 km. When do they meet?
• A wholesaler marks up goods by 50% and gives a 12% trade discount. A retailer marks up by 20% and offers an 8% discount. The customer pays ₹12,216. What is the wholesaler's cost price approximately?
• If A : B = 3 : 4, B : C = 5 : 6, and C : D = 7 : 8, then find B : D.
• What is the result of $3^2 + 5 \div 0.8$?

⚔️ Practice SSC CGL (Prelims) General free + battle 1v1 →