# the first three terms in the expansion of (x+y)^n are 1,56,1372 respectively.Find x and y

Expansion of (x+y)n upto 3 term
${n}_{{C}_{0}}{x}^{n}+{n}_{{C}_{1}}{x}^{n-1}y+{n}_{{C}_{2}}{x}^{n-2}{y}^{2}+......$
So we are given

and

From equation (i) we have
${x}^{n}=1\phantom{\rule{0ex}{0ex}}⇒{x}^{8}=1\phantom{\rule{0ex}{0ex}}⇒x=1$
From equation(ii) we have
$\frac{ny}{x}=56\phantom{\rule{0ex}{0ex}}⇒8y=56\phantom{\rule{0ex}{0ex}}⇒y=7$
So x=1, y =7, n=8

• 56

x = 1 , y = 7

n = 8

Very long proof.

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• 7
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