$ab + bc$ $= 130$
$bc + ca$ $= 168$
$ca + ab$ $= 228$
Find the value of $a + b + c$ from the given set of equations
Blended with equations
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- Kazi_Zareer
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Re: Blended with equations
Given that,
$ab+bc =130 ... ... ... ... ...$ (i)
$bc+ca =168 ... ... ... ... ...$ (ii)
$ca+ab =228 ... ... ... ... ...$ (iii)
Sum this three equation and you will get,
$ 2 (ab + bc + ca ) = 586 $
$\Rightarrow ab + bc + ca = 263 ... ... ... ... ...$ (iv)
From (i) and (iv) we get,
$ 130 + ca = 263 $ $[\because ab+bc =130]$
$\Rightarrow ca = 263 - 130 = 133 = 7 \times 19 $
Again, from (ii) and (iv) we get,
$ ab + 168 = 263 $ $[\because bc + ca =168]$
$\Rightarrow ab = 263 - 168 = 95 = 5 \times 19 $
Now look at this, $ ca = 7 \times 19 $ and $ ab = 5 \times 19 $ . Now the rest goes up to you.
$ab+bc =130 ... ... ... ... ...$ (i)
$bc+ca =168 ... ... ... ... ...$ (ii)
$ca+ab =228 ... ... ... ... ...$ (iii)
Sum this three equation and you will get,
$ 2 (ab + bc + ca ) = 586 $
$\Rightarrow ab + bc + ca = 263 ... ... ... ... ...$ (iv)
From (i) and (iv) we get,
$ 130 + ca = 263 $ $[\because ab+bc =130]$
$\Rightarrow ca = 263 - 130 = 133 = 7 \times 19 $
Again, from (ii) and (iv) we get,
$ ab + 168 = 263 $ $[\because bc + ca =168]$
$\Rightarrow ab = 263 - 168 = 95 = 5 \times 19 $
Now look at this, $ ca = 7 \times 19 $ and $ ab = 5 \times 19 $ . Now the rest goes up to you.
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