Algebra — practice questions with answers
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If x + 1/x = 4 , find the value of x^2 + 1/x^2 .If x⁴ + 1/x⁴ = 119 and x > 1, find the value of x³ − 1/x³.If 3x + 1/2x = 5, find the value of 9x^2 + 1/4x^2.If x + 1/x = 1, find the value of x⁹⁹ + 1/x⁹⁹.If x = √3 + √2, find the value of x³ + 1/x³.If x = 3 + 2√2, find the value of √x + 1/√x.If a + b = 12 and a² + b² = 80, find a³ + b³.If a + b + c = 9, ab + bc + ca = 26 and abc = 24, find a³ + b³ + c³.Given a + b + c = 15 and a² + b² + c² = 83, find a³ + b³ + c³ − 3abc.If a = 101, b = 99 and c = 100, what is a³ + b³ + c³ − 3abc?Express in factored form: (a^2-b^2)^3 + (b^2-c^2)^3 + (c^2-a^2)^3/(a-b)^3 + (b-c)^3 + (c-a)^3If x² + y² + z² − xy − yz − zx = 0 and x = 5, find x + y + z (x, y, z real).For real a, b, c with a² + b² + c² = 2(a − b − c) − 3, find 2a − 3b + 4c.If 2x + 3y = 13 and 5x − 2y = 4, what is x + y?At a fair, 2 adult tickets and 3 child tickets cost ₹340, while 3 adult tickets and 2 child…What is the area of the triangle formed by the lines x + y = 6, x − y = 2 and the y-axis?ax³ + bx² + x − 6 has (x + 2) as a factor and leaves remainder 36 when divided by (x − 2). Find a…The zeroes of x³ − 12x² + 39x − k are in arithmetic progression. What is k?Which is the largest: √2, ∛3, ⁴√5, ⁶√10?The value of (x^(a−b))^(a+b) × (x^(b−c))^(b+c) × (x^(c−a))^(c+a) is:For x > 0 with x⁴ + 1/x⁴ = 47, what is x³ + 1/x³?Given x + 1/x = −2, evaluate x²⁰²⁵ + 1/x²⁰²⁵.Let x = 1/(2 − √3). Find the value of x³ − 2x² − 7x + 5.Two numbers have sum 9 and product 18. What is a/b + b/a?Numbers x and y (x > y) have sum 15 and product 54. Compute x² − y².
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