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Question

If x=23-5and y=23+5, then x + y = __________.

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Solution

Given:x=23-5y=23+5Now,x=23-5Multiply and divide RHS by 3+5, we getx=23-5×3+53+5x=23+532-52 Using the identity:a+ba-b=a2-b2x=23+53-5x=23+5-2x=-3+51x=-3-5y=23+5Multiply and divide RHS by 3-5, we gety=23+5×3-53-5y=23-532-52 Using the identity:a+ba-b=a2-b2y=23-53-5y=23-5-2y=-3-51y=-3+5Thus,x+y=-3-5+-3+5 =-3-5-3+5 =-23 =-23


Hence, x + y = -23.

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