Solve a^2 b^2 = c^2 3^2 10^2 = c^2 - ScanMath

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Type your math problem... a^2 b^2 = c^2 3^2 10^2 = c^2

Question

Solve the system of equations

(a_{1}, b_{1}, c_{1}) = (0, b, 0), b \in R (a_{2}, b_{2}, c_{2}) = (a, 0, 0), a \in R

Evaluate

{a^{2} b^{2} = c^{2} \times 3^{2} \times 1 0^{2} c^{2} \times 3^{2} \times 1 0^{2} = c^{2}

Calculate

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{a^{2} b^{2} = 3 0^{2} c^{2} c^{2} \times 3^{2} \times 1 0^{2} = c^{2}

Calculate

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{a^{2} b^{2} = 3 0^{2} c^{2} 3 0^{2} c^{2} = c^{2}

Solve the equation for c

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{a^{2} b^{2} = 3 0^{2} c^{2} c = 0

Substitute the given value of c into the equation a^{2} b^{2} = 3 0^{2} c^{2}

a^{2} b^{2} = 3 0^{2} \times 0^{2}

Simplify

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a^{2} b^{2} = 0

Separate the equation into 2 possible cases

a^{2} = 0 \cup b^{2} = 0

The only way a power can be 0 is when the base equals 0

a = 0 \cup b^{2} = 0

The only way a power can be 0 is when the base equals 0

a = 0 \cup b = 0

Rearrange the terms

{a = 0 c = 0 \cup {b = 0 c = 0

Check the solution

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{a = 0 c = 0 \cup {b = 0 c = 0

Check the solution

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{a = 0 c = 0 \cup {b = 0 c = 0

Solution

(a_{1}, b_{1}, c_{1}) = (0, b, 0), b \in R (a_{2}, b_{2}, c_{2}) = (a, 0, 0), a \in R

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