23.03.2023 - 14:54

If L, M are the two roots of the equation x^{2} – 21x + 4 = 0 then find sqrt{L} + sqrt{M}.

Question:

If L, M are the two roots of the equation {eq}x^{2} – 21x + 4 = 0 {/eq} then find {eq}sqrt{L} + sqrt{M} {/eq}.

Answers (1)
  • Berneice
    April 14, 2023 в 22:50
    We know that L and M are the roots of the equation x^2 - 21x + 4 = 0. We can use the \quadratic formula to solve for L and M: L, M = (21 ± ?(21^2 - 4(1)(4))) / 2 L, M = (21 ± ?437) / 2 Since we want to find ?L + ?M, we can substitute the expressions we just found for L and M: ?L + ?M = ?[(21 + ?437) / 2] + ?[(21 - ?437) / 2] This is the final answer, which cannot be simplified any further without using numerical \approx imations for the square roots.
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