Question

If x + y = √5 and x-y = √2, show that 8xy (x² + y²) = 21


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Answer 1

Answer:

= 4√15. Answer

Step-by-step explanation:

8xy(x^2-y^2) = ? given that

x+y = √5 …(1) and

x-y = √3 …(2)

Multiply (1) and (2) to get (x^2-y^2) = √15

Add (1) and (2) to get 2x = (√5 + √3) …(3)

Subtract (2) from (1) to get 2y = (√5 - √3) …(4)

Therefore, 8xy(x^2-y^2) = 2*2x*2y*(x^2-y^2)

= 2*(√5 + √3)*(√5 - √3)*√15

= 2*2*√15

= 4√15. Answer

Answer 2

Answer:

21(proved)

Step-by-step explanation:

x + y = √5

x - y = √2

_________

2x =√5+√2

x = √5+√2/ 2

y= √5-√2/ 2

xy = 3/4 ( multiplying)

8xy (x² + y²)

= 2× 4xy (x² + y²)

= 2× ((x+y)^2– (x-y)^2) {(x-y)^2 + 2xy}

= 2× ( 5-2)(2+ 2×3/4)

= 2×3×7/2

= 21