Question

If 9x² + y² = 13 and xy = 2, find the value of
(i) 3x + y, (ii) 3x - y.​

Answer 1

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• 9x² + y² = 13

• xy = 2

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• Value of 3x + y and 3x - y

Formula to be used :-

• (a - b)² = a² + b² - 2ab

• (a + b)² = a² + b² + 2ab

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Given that,

• 9x² + y² = 13

• xy = 2

____________________________________________________

Now, find the value of 3x + y.

⟶ ( 3x + y) ²

= (3x)² + y² + 2 × 3x × y

= 9x² + y² + 6xy

(Putting given values)

= 13 + 6 × 2

= 25

⟶ ( 3x + y)² = 25

⟶ 3x +y = √25

⟶ 3x + y = 5

_________________________________________________

Again,

⟶ (3x - y)²

= ( 3x)² - 2 × 3x × y + y²

= 9x² + y² - 6 xy

= 13 - 6 ×2

= 1

⟶ (3x - y)² = 1

⟶ 3x - y = 1

_________________________________________________

Therefore,

Hence , value of 3x + y = 5

Value of 3x - y = 1

Answer 2

Answer:

{ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}

GivEn:

• 9x² + y² = 13

• xy = 2

{ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}

Tofind:

• Value of 3x + y and 3x - y

Formula to be used :-

• (a - b)² = a² + b² - 2ab

• (a + b)² = a² + b² + 2ab

{ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}

SoluTion:

Given that,

• 9x² + y² = 13

• xy = 2

____________________________________________________

Now, find the value of 3x + y.

⟶ ( 3x + y) ²

= (3x)² + y² + 2 × 3x × y

= 9x² + y² + 6xy

(Putting given values)

= 13 + 6 × 2

= 25

⟶ ( 3x + y)² = 25

⟶ 3x +y = √25

⟶ 3x + y = 5

_________________________________________________

Again,

⟶ (3x - y)²

= ( 3x)² - 2 × 3x × y + y²

= 9x² + y² - 6 xy

= 13 - 6 ×2

= 1

⟶ (3x - y)² = 1

⟶ 3x - y = 1

_________________________________________________

Therefore,

Hence , value of 3x + y = 5

Value of 3x - y = 1