Question

answer in full step pls​

Answer 1

Answer:

x = 0 or x = -a

Step-by-step explanation:

(a + x + root(a^2-x^2))/(a + x - root(a^2-x^2)) = b/x

Multiplying both numerator and denominator by  (a + x + root(a^2-x^2),

(a + x + root(a^2-x^2))^2/((a + x)^2 - (root(a^2-x^2))^2) = b/x

=((a + x)^2 + a^2 - x^2 +2(a + x)root(a^2 - x^2))/a^2 + x^2 +2ax - a^2 + x^2 = b/x

=(a^2 + x^2 + 2ax + a^2 - x^2 +2(a + x)root(a^2 - x^2))/(2x^2 + 2ax) = b/x

=(a^2 + ax + (a + x)root(a^2 - x^2))/x^2 + ax = b/x

Cross multiplying,

xa^2 + ax^2 + ax*root(a^2 - x^2) + x^2*root(a^2 - x^2) = bx^2 + abx

Bringing all the terms to one side and grouping the common terms,

x^2[a + root(a^2 - x^2) - b] + xa[a + root(a^2 - x^2) - b] = 0

x(x + a)(a + root(a^2 - x^2) - b) = 0

x = 0 or x = -a

Answer 2

Answer:

x = 0 or x = -a

Step-by-step explanation:

(a + x + root(a^2-x^2))/(a + x - root(a^2-x^2)) = b/x

Multiplying both numerator and denominator by  (a + x + root(a^2-x^2),

(a + x + root(a^2-x^2))^2/((a + x)^2 - (root(a^2-x^2))^2) = b/x

=((a + x)^2 + a^2 - x^2 +2(a + x)root(a^2 - x^2))/a^2 + x^2 +2ax - a^2 + x^2 = b/x

=(a^2 + x^2 + 2ax + a^2 - x^2 +2(a + x)root(a^2 - x^2))/(2x^2 + 2ax) = b/x

=(a^2 + ax + (a + x)root(a^2 - x^2))/x^2 + ax = b/x

Cross multiplying,

xa^2 + ax^2 + ax*root(a^2 - x^2) + x^2*root(a^2 - x^2) = bx^2 + abx

Bringing all the terms to one side and grouping the common terms,

x^2[a + root(a^2 - x^2) - b] + xa[a + root(a^2 - x^2) - b] = 0

x(x + a)(a + root(a^2 - x^2) - b) = 0

x = 0 or x = -a

Step-by-step explanation: