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Algebra and Applications Test 3

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Question : 4 of 25

Marks: +1, -0

If

ax + by = 3

bx - ay = 4

x^2 + y^2 = 1

, then the value of

a^2 + b^2

is:

1
25
-1
-25

Solution:

ax + by = 3

bx - ay = 4

and

x^2 + y^2 = 1

From the above equation, it is clear that the values of x and y are

\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}

respectively

Now,

\frac{a}{\sqrt{2}}+\frac{b}{\sqrt{2}}=3

\frac{b}{\sqrt{2}}-\frac{a}{\sqrt{2}}=4

a+b=3\sqrt{2}

......(i)

b-a=4\sqrt{2}

......(ii)

Squaring both the sides of equation (i) and (ii) and adding we get:

2(a^2+b^2)=50

Value of

a^2+b^2=25

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