51. If x+y=9 and xy = 12, then find the
value of x2 + y2
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If x + y = 9 and xy = 12 then x² + y² = 57
Given :
x + y = 9 and xy = 12
To find :
The value of x² + y²
Formula :
(x + y)² = x² + 2xy + y²
Solution :
Step 1 of 2 :
Write down the given values
Here it is given that x + y = 9 and xy = 12
Step 2 of 2 :
Find the value of x² + y²
(x + y)² = x² + 2xy + y²
⇒ 9² = x² + y² + 2xy
⇒ 81 = x² + y² + ( 2 × 12 )
⇒ 81 = x² + y² + 24
⇒ x² + y² = 81 - 24
⇒ x² + y² = 57
Hence the value of x² + y² = 57
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