Question

if 2(x-y)²=16 and xy=24, find the value of x²+y²​

Answer 1

ANSWER:

• Value of x²+y² = 56.

GIVEN:

• 2(x-y)²=16
• xy = 24 ....(i)

TO FIND:

• Value of x²+y².

SOLUTION:

=> 2(x-y)² = 16

=> (x-y)² = 16/2

=> (x-y)² = 8

=> x²+y²-2xy = 8

Putting xy = 24 from (i)

=> x²+y²-2(24) = 8

=> x²+y²-48 = 8

=> x²+y² = 8+48

=> x²+y² = 56.

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab

Answer 2

Step-by-step explanation:

2$(x-y)^{2}$ =16

2($x^{2}$ +$y^{2}$ -2xy) =16

($x^{2}$ +$y^{2}$ -2xy) = 16/2 = 8

($x^{2}$ +$y^{2}$) = 8 +2xy

           = 8 +2(24)

            = 8 + 48

($x^{2}$ +$y^{2}$)  = 56

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