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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:

Concept:

Square and add the two given equations to form

(a^2+b^2)(x^2+y^2)

.

Explanation:

Given

ax+by=3

and

bx-ay=4

.

Square both and add:

(ax+by)^2+(bx-ay)^2=3^2+4^2

.

So,

(ax+by)^2+(bx-ay)^2=25

.

Expand the left side:

a^2x^2+2abxy+b^2y^2+b^2x^2-2abxy+a^2y^2

.

Combine like terms:

a^2(x^2+y^2)+b^2(x^2+y^2)=25

.

Factor out

(x^2+y^2)

:

(a^2+b^2)(x^2+y^2)=25

.

Given

x^2+y^2=1

.

Thus,

a^2+b^2=25

.

Answer:

25

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