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If x + y = 10 and xy = 21, what is the value of x┬▓ + y┬▓?
58
62
42
100
58
Mentally think of two numbers whose sum is 10 and product is 21 (7 and 3), then immediately square them to get 49 + 9 = 58.
Sum of two numbers x + y = 10 and their product xy = 21
(x+y)2=x2+y2+2xy
Mentally think of two numbers whose sum is 10 and product is 21 (7 and 3), then immediately square them to get 49 + 9 = 58.
Students often wrongly compute (x+y)2 as x2+y2 and forget to subtract 2xy, or make calculation errors with squares.
Write the standard algebraic identity
Start with the square of the binomial sum formula relating x+y, xy, and x2+y2.
(x+y)2=x2+y2+2xy
Substitute the given values
Substitute x+y=10 and xy=21 into the identity.
(10)2=x2+y2+2(21)
Simplify and calculate
Evaluate the square and product terms to isolate x2+y2.
100=x2+y2+42
Find the final value
Subtract 42 from 100 to determine the value of x2+y2.
x2+y2=100тИТ42=58
A is correct because the calculated value of x2+y2 is 58.
Recognizing standard algebraic identities is crucial for quadratic equations and polynomial factorization problems in railway and banking exams.
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