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Home » Use the identity: \( x^2 + y^2 = (x + y)^2 - 2xy \) - Veritas Home Health

Use the identity: \( x^2 + y^2 = (x + y)^2 - 2xy \) - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Express 81 as \( 3^4 \), so equation becomes:
\( 3^{2x+1} = 3^4 \cdot 3^{x-1} = 3^{4 + x - 1} = 3^{x+3} \).
Since bases are equal, set exponents equal:
\( 2x + 1 = x + 3 \) → \( 2x - x = 3 - 1 \) → \( x = 2 \).
In a triangle, the lengths of two sides are 13 cm and 15 cm. If the an...
Use the Law of Cosines: \( c^2 = a^2 + b^2 - 2ab\cos C \), where \( a...
\( c^2 = 13^2 + 15^2 - 2 \cdot 13 \cdot 15 \cdot 0.5 = 169 + 225 - 195...
So, \( c = \sqrt{199} \approx 14.106 \), but we keep exact: \( \sqrt{1...
However, for exact boxed answer: \( \sqrt{199} \) is simplest.
But compute: \( 169 + 225 = 394 \), \( 2 \cdot 13 \cdot 15 = 390 \), \...

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