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

By Peyton

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

About the author
Peyton

Why can it be argued that the Warsaw Pact was less of a defensive alliance and more of a means to control the Soviet satellite sta

Direction : Write the different ways on which we can
provide evidence to support opinion or fact.
1.
CHA WN-​

2 thoughts on “If x² + y² + 10 = 2 √2 x + 4 √2 y, <br /> then find the value of ( x + y ).”

  2. 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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