Algebra — practice questions, page 2
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If a + b = 5 and ab = 6, what is a⁵ + b⁵?For a = 25, b = 15 and c = −10, evaluate a³ + b³ + c³ − 3abc.Numbers a, b, c satisfy a + b + c = 6, ab + bc + ca = 11 and abc = 6. Find a³ + b³ + c³.Real numbers satisfy (x − 3)² + (y − 4)² + (z + 2)² = 0. What is x + y + z?For real a, b, c with a² + b² + c² = ab + bc + ca and a + b + c = 18, find abc.Three numbers have a + b + c = 9, ab + bc + ca = 23 and abc = 15. Find a²b² + b²c² + c²a².Given x − y = 2 and y − z = 3, find (x − y)³ + (y − z)³ + (z − x)³.Let x = (√3 + √2)/(√3 − √2) and y = (√3 − √2)/(√3 + √2). Find x² + xy + y².Find the value of 1/(√2 + 1) + 1/(√3 + √2) + 1/(√4 + √3).Two numbers add up to 9 and the sum of their squares is 41. What is the sum of their cubes?For a = 2026, b = 2025 and c = 2024, find a³ + b³ + c³ − 3abc.Non-zero numbers a and b satisfy a/b + b/a = 1. What is a³ + b³?The numbers a, b, c satisfy a + b + c = 10 and ab + bc + ca = 31. Find a³ + b³ + c³ − 3abc.The denominator of a fraction is 4 more than its numerator. When 3 is added to both, the fraction…A two-digit number equals 4 times the sum of its digits, and its units digit is 3 more than its…If x/2 + y/3 = 4 and x/3 + y/2 = 13/3, find xy.Solve 2/x + 3/y = 13 and 5/x − 4/y = −2, and find x + y.Find k so that 4x + 6y = 11 and 2x + ky = 7 have no solution.Five pens and three notebooks cost ₹155; three pens and five notebooks cost ₹165. What does one…2 kg apples and 1 kg grapes cost ₹310, and 4 kg apples and 2 kg grapes cost ₹620. How many (price…The sum of a two-digit number and the number formed by reversing its digits is 121. The digits…A taxi charges a fixed amount plus a rate per km. A 10 km ride costs ₹205 and a 15 km ride costs…Find the area of the triangle formed by the lines 2x + 3y = 12, x − y = 1 and the x-axis.A sum of ₹1,000 is made up of ₹50, ₹20 and ₹10 notes, 40 notes in all. There are twice as many ₹20…Which equation has roots that are the reciprocals of the roots of 3x² − 7x + 2 = 0?
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