Find two consecutive even numbers whose sum of the squares is 1060
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Hi there!
Here's the answer:
Let 2 consecutive even no.s be 'x' and 'x+2'.
Given, their sum of squares = 1060
x²+(x+2)² = 1060
=> x² + x² + 4x + 4 = 1060
=> 2x² + 4x - 1056 = 0
=> x² + 2x - 528= 0
=> x² +24x - 22x - 528= 0
=> x(x+24)-22(x+24)= 0
=> (x-22)(x+24)= 0
•°• x= 22 or -24
•°• x= 22 & x+2= 24
•°• The 2 consecutive Even no.s are 22,24.
Here's the answer:
Let 2 consecutive even no.s be 'x' and 'x+2'.
Given, their sum of squares = 1060
x²+(x+2)² = 1060
=> x² + x² + 4x + 4 = 1060
=> 2x² + 4x - 1056 = 0
=> x² + 2x - 528= 0
=> x² +24x - 22x - 528= 0
=> x(x+24)-22(x+24)= 0
=> (x-22)(x+24)= 0
•°• x= 22 or -24
•°• x= 22 & x+2= 24
•°• The 2 consecutive Even no.s are 22,24.
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