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Step-by-step explanation:
Answer:
nx² - 2mx + n = 0
Step-by-step explanation:
If x = square root of (m+n)+square root of (m-n)/square root of (m+n)-square root (m-n), where n which isn't equal 0 , then find the value of nx^2 - 2mx + n.
\begin{gathered}x = \frac{\sqrt{m + n} + \sqrt{m-n}}{\sqrt{m + n} - \sqrt{m-n}}\\ \\Multiplying \: \& \: divide\: by \: \sqrt{m + n} + \sqrt{m-n}\\ \\x = \frac{\sqrt{m + n} + \sqrt{m-n}}{\sqrt{m + n} - \sqrt{m-n}} \times \frac{\sqrt{m + n} + \sqrt{m-n}}{\sqrt{m + n} + \sqrt{m-n}} \\ \\\\x = \frac{m + n + m - n + 2\sqrt{m^2 - n^2} }{m + n - (m-n) } \\ \\x = \frac{2(m + \sqrt{m^2 - n^2})}{2n} \\ \\x = \frac{m + \sqrt{m^2 - n^2}}{n} \\ \\nx = m + \sqrt{m^2 - n^2} \\ \\nx - m = \sqrt{m^2 - n^2} \\\end{gathered}
x=
m+n
−
m−n
m+n
+
m−n
Multiplying÷by
m+n
+
m−n
x=
m+n
−
m−n
m+n
+
m−n
×
m+n
+
m−n
m+n
+
m−n
x=
m+n−(m−n)
m+n+m−n+2
m
2
−n
2
x=
2n
2(m+
m
2
−n
2
)
x=
n
m+
m
2
−n
2
nx=m+
m
2
−n
2
nx−m=
m
2
−n
2
squaring both sides
(nx-m)² = m² - n²
=> n²x² + m² - 2mnx = m² - n²
=> n²x² - 2mnx = - n²
Diving by n both sides
=> nx² - 2mx = - n
=> nx² - 2mx + n = 0