Solve the equation x - b x - c-a - b a - c - x - cx - a-b - c b - a - x - a x - b-c - a c - b - 1-

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Byju's Answer

Standard VIII

Mathematics

Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

Solve the equ...

Question

Solve the equation
$\frac{(x - b) (x - c)}{(a - b) (a - c)} + \frac{(x - c) (x - a)}{(b - c) (b - a)} + \frac{(x - a) (x - b)}{(c - a) (c - b)} = 1.$

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Solution

values of x are a,b,c
substituting these values one of the terms become one and other two become zero

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Similar questions

Q. The quadratic equation

\frac{(x + b) (x + c)}{(b - a) (c - a)} + \frac{(x + c) (x + a)}{(c - b) (a - b)} + \frac{(x + a) (x + b)}{(a - c) (b - c)} = 1

has

Q. Prove that

\frac{(x - b) (x - c)}{(a - b) (a - c)} + \frac{(x - c) (x - a)}{(b - c) (b - a)} + \frac{(x - a) (x - b)}{(c - a) (c - b)} = 1

Let $ϕ (x) = \frac{(x - b) (x - c)}{(a - b) (a - c)} f (a) + \frac{(x - c) (x - a)}{(b - c) (b - a)} f (b) + \frac{(x - a) (x - b)}{(c - a) (c - b)} f (c) - f (x)$ Where a < c < b and $f^{11} (x)$ exists at all points in (a,b) . Then, there exists a real number $μ$ a < $μ$ < b such that $\frac{f (a)}{(a - b) (a - c)} + \frac{f (b)}{(b - c) (b - a)} + \frac{f (c)}{(c - a) (c - b)} =$

Q. Suppose a, b, c are three distinct real numbers. Let

P (x) = \frac{(x - b) (x - c)}{(a - b) (a - c)} + \frac{(x - c) (x - a)}{(b - c) (b - a)} + \frac{(x - a) (x - b)}{(c - a) (c - b)}

When simplified,

P (x)

becomes

Q. Suppose

a, b, c

are three distinct real numbers. Let

P (x) = \frac{(x - b) (x - c)}{(a - b) (a - c)} + \frac{(x - c) (x - a)}{(b - c) (b - a)} + \frac{(x - a) (x - b)}{(c - a) (c - b)}

when simplified

P (x)

becomes

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Solve the equation (x−b)(x−c)(a−b)(a−c)+(x−c)(x−a)(b−c)(b−a)+(x−a)(x−b)(c−a)(c−b)=1.

values of x are a,b,csubstituting these values one of the terms become one and other two become zero

Solve the equation
$\frac{(x - b) (x - c)}{(a - b) (a - c)} + \frac{(x - c) (x - a)}{(b - c) (b - a)} + \frac{(x - a) (x - b)}{(c - a) (c - b)} = 1.$

values of x are a,b,c
substituting these values one of the terms become one and other two become zero