Question

If x² + y² + 10 = 2 √2 x + 4 √2 y,
then find the value of ( x + y ).

Answer 1

QuestioN :

If x² + y² + 10 = 2 √2 x + 4 √2 y,  then find the value of ( x + y ).

GiveN :

• x² + y² + 10 = 2√2 x + 4√2 y

To FiNd :

• Value of (x + y)

FormulA :

• a² - 2ab + b² = (a - b)²

ANswer :

Value of (x + y) = 3√2

SolutioN :

⇒ x² + y² + 10 = 2√2 x + 4√2 y

⇒ x² + y² + 10 - 2√2 x - 4√2 y = 0

Rearranging the terms,

⇒ x² - 2√2 x + y² - 4√2 y + 10 = 0

⇒ (x)² - 2*(√2)*(x) + (y)² - 2*(2√2)*(y) + 10 = 0

Adding and subtracting both (√2)² and (2√2)²

⇒ (x)² - 2*(√2)*(x) + (y)² - 2*(2√2)*(y) + 10 + (√2)² - (√2)² + (2√2)² - (2√2)²= 0

Rearranging the terms,

⇒ [(x)² - 2*(√2)*(x) + (√2)²] + [(y)² - 2*(2√2)*(y) + (2√2)²] + [10 - (√2)² - (2√2)²]= 0

We know that,

a² - 2ab + b² = (a - b)²

So,

⇒ [x - √2]² + [y - 2√2]² + [10 - 2 - 8] = 0

⇒ [x - √2]² + [y - 2√2]² + 10 - 10 = 0

⇒ [x - √2]² + [y - 2√2]² = 0

⇒ [x - √2]² = - [y - 2√2]²

⇒ [x - √2]² = [2√2 - y]²

Square rooting both sides,

⇒ x - √2 = 2√2 - y

⇒ x + y = 2√2 + √2

⇒ x + y = 3√2

∴Hence, Value of (x + y) = 3√2.

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Answer 2

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