Question

if x²-y²=8 and x-y=2 then find the value of y​

Answer 1

Answer

y=2

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Step-by-step explanation:

${x}^{2} - {y}^{2} = 8 \\ x - y =2 \\ Using \: basic \: identity \\ {x}^{2} - {y}^{2} = (x + y)(x - y) \\ Using \: this \: identity \\ (x + y)(x - y) = 8 \\ Putting \: the \: value \: of \: (x - y) \\ 2(x + y) = 8 \\ = > (x + y) = \frac{8}{2} \\ = > (x + y) = 4 \\ So, \: we \: get \: two \: equations \: here \: .. \\ (x - y) = 2.......(1) \\ (x + y) = 4.......(2) \\ Subtracting \: (2) \ \: from \: \: (1) \\ - 2y = 2 - 4 \\ = > - 2y = - 2 \\ = > y = \frac{ - 2}{ - 2} \\ = > y = 1$

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Hope it helps !!!

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~Soumok

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Answer 2

Step-by-step explanation:

Given -

x² - y² = 8

x - y = 2

To Find -

Value of y

Now,

x - y = 2

• x = 2 + y

Substituting the value of x = 2 + y on

x² - y² = 8

= (2 + y)² - y² = 8

= (2)² + 2 × 2 × y + (y)² - y² = 8

= 4 + 4y + y² - y² = 8

= 4y = 8 - 4

= 4y = 4

• y = 1

Substituting the value of y = 1 on x - y = 2

x - 1 = 2

x = 2 + 1

x = 3

Hence,

Value of x = 3 , and y = 1

Formula used -

• (a + b)² = a² + 2ab + b²

Other formula like this -

• (a - b)² = a² - 2ab + b²
• (a + b)(a - b) = a² - b²
• (a + b)³ =
• a³ + 3a²b + 3b²a + b³
• (a - b)³ =
• a³ - 3a²b + 3b²a - b³