Question

(e)) If a+b+c= 12 and a² + b2 + c = 64, find the value of ab + bc + ac
bhai bol do ​

Answer 1

Step-by-step explanation:

Here, we having two equations

a + b + c = 12 ...(eq.1)

a^2 + b^2 + c^ =64 …(eq.2)

by eq.1 we can calculate the value of a, b & c as

a = 12 - b - c

b = 12 - a - c

c = 12 - a - b

then we put the value of a in second equation.

we get,

(12 - b - c)^2 + b^2 + c^2 = 64

after solving this,

we get, b^2 + bc + c^2 - 12b - 12c + 40 =0

by using above equation we calculate the term bc.

therefore, bc = 12b + 12c - b^2 -c^2 - 40

similarly by putting the values of b and c in eq.2 we get,

ac = 12a + 12c - a² - c² - 40

ab = 12a + 12b - a² - b² - 40

and now,

ab + bc + ac = (12a + 12b - a² - b² - 40) + (12b + 12c - b² -c² - 40) + (12a + 12c - a² - c² - 40)

ab + bc + ac = 24a + 24b + 24c - 2a² - 2b² – 2c² – 120

ab + bc + ac = 24( a + b + c ) - 2(a²+ b²+ c²) - 120

by eq.1 and eq.2,

ab + bc + ac = 24(12) - 2(64) - 120

ab + bc + ac = 40

Hence, ab + bc + ac = 40

Answer 2

Answer:

${ \bold{ {( a +b +c )}^{2}= {a}^{2} + {b}^{2} + {c}^{2}+2(ab +bc+ac)}}$

${ \bold{ \implies{ {(12)}^{2} = 64 + 2(ab + bc + ca)}}}$

${ \bold{ \implies{ 144 = 64 + 2( ab + bc + ac)}}}$

${ \bold{ \implies{ 2(ab + bc + ac) = 144 - 64}}}$

${ \bold{ \implies{2(ab + bc + ac) = 80}}}$

${ \bold{ \implies{ (ab + bc + ac) = 40}}}$

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