Question

if x+y=7/2 and xy=5/2 find x^2-y^2​

Answer 1

Answer:

${x} + y = 7 \div 2$

squaring on both sides

${(x + y) }^{2} = 7 \div 2$

${x}^{2} + {y}^{2} + 2xy = {(7 \div 2)}^{2}$

${x}^{2} + {y}^{2} + 2 \times 5 \div 2 = 49 \div 4$

${x}^{2} + {y}^{2} + 5 = 49 \div 4$

${x}^{2} + {y}^{2} = 49 \div 4 - 5$

solve it then you will get the answer

Step-by-step explanation:

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Answer 2

Answer: 21/4

Step-by-step explanation:

(x+y)^2 = x^2 + y^2 + 2xy

(7/2)^2 = x^2 + y^2 + 2(5/2)

x^2 + y^2 = 49/4 - 5 = 29/4

(x-y)^2 = x^2 + y^2 - 2xy

(x-y)^2 = 29/4 - 5 = 9/4

x-y = √9/4 = 3/2

Now,

x^2 - y^2 = (x+y)(x-y)

= 3/2 × 7/2

= 21/4