What is the answer to xc=(a(xa)+b(xb))/(a+b) ?

The answer to xc=(a(xa)+b(xb))/(a+b) is x=0;\quad a+b\ne 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

xc=(a(xa)+b(xb))/(a+b)

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

x = 0; a + b \neq = 0

Solution steps

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

Multiply both sides by

a + b

x c (a + b) = a^{2} x + b^{2} x; a + b \neq = 0

Subtract

a^{2} x + b^{2} x

from both sides

x c (a + b) - (a^{2} x + b^{2} x) = a^{2} x + b^{2} x - (a^{2} x + b^{2} x); a + b \neq = 0

Simplify

c a x + c b x - a^{2} x - b^{2} x = 0; a + b \neq = 0

Factor

c a x + c b x - a^{2} x - b^{2} x : x (c a + c b - a^{2} - b^{2})

x (c a + c b - a^{2} - b^{2}) = 0; a + b \neq = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0; a + b \neq = 0

9 (- 74 y + 76) = 8 (- 81 y - 27)

10 k + 7 = - 3 - 10 k

- 15 = - 5 w

- \frac{3}{2} w = 17

2 = w + 9

What is the answer to xc=(a(xa)+b(xb))/(a+b) ?
The answer to xc=(a(xa)+b(xb))/(a+b) is x=0;\quad a+b\ne 0