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Examoogle • User • info@examoogle.com • EE-2024-8821
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If A+B = 10 and AB = 21, find the value of A² + B².
58
62
48
52
58
Given: Sum of two numbers A + B = 10, Product of two numbers AB = 21
Sum of two numbers A + B = 10, Product of two numbers AB = 21
(A+B)2=A2+B2+2AB
Identify two numbers that add to 10 and multiply to 21 · Mentally, these are 7 and 3 · Then, calculate 72+32=49+9=58.
Many students mistake A2+B2 for (A+B)2 and incorrectly select 102=100.
Write the identity
Use the standard algebraic expansion for the square of a binomial: (A+B)2=A2+B2+2AB.
(A+B)2=A2+B2+2AB
Substitute the values
Substitute A+B=10 and AB=21 into the identity to isolate the unknown A2+B2.
(10)2=A2+B2+2(21)
Solve for the expression
Evaluate the powers and products, then subtract to find the final value: 100=A2+B2+42, so A2+B2=100−42.
A2+B2=58
A is correct because substituting the given values into the algebraic identity results in 100−42=58.
This concept is a precursor to solving quadratic equations via the sum and product of roots (Vieta's formulas), which is frequently tested in RRB exams.