Question

If a + b = 100 and a^2 + b^2 = 436,find the value of a^3 + b^3. ​

Answer 1

Answer:

$\huge{\pink{\green {\sf\boxed{\therefore -434600}}}}$

Step-by-step explanation:

$\bold{\underline {Given:}}$

• ${a + b = 100}$
• ${a}^{2} + {b}^{2} ={436}$

$\bold{\underline {To\:Find:}}$

$⟹ {Value \:of \:{a}^{3} +{b}^{3} =?}$

$\huge {\red{\boxed{SOLUTION⟹}}}$

We know that ${a + b}^{2} = {a}^{2}{b}^{2} + {2ab}$

Putting ${a + b} = {100}$ and ${{a}^{2} + {b}^{2}} = {436}$, we get :

$⟹ {(100)}^{2} = {436 + 2ab}$

$⟹ {10000} = {436 + 2ab}$

$⟹ {2ab} = {-436 + 10000}$

$⟹ {2ab} = {9564}$

$⟹ {ab} = {\dfrac{9564}{2}}$

$⟹ {ab} = {4782}$

$\Large\boxed{Now}$

$⟹ {(a + b)}^{3} = {{a}^{3} + {b}^{3}} + {3ab (a + b)}$ ${[ ∴ a + b = 100\: and \:ab = 4782]}$

$⟹ {(100)}^{3} = {{a}^{3} + {b}^{3}} + {3*4782*100}$

$⟹ {1000000} = {{a}^{3} + {b}^{3}} + {1432600}$

$⟹ {1000000 - 1434600} = {{a}^{3} + {b}^{3}}$

$⟹ {{a}^{3} + {b}^{3}} = {-434600}$

$\huge {\red{\boxed{Thus,{a}^{3} + {b}^{3} = -434600}}}$

$\Large\boxed{SOLVED}$

#Be_Brainly

Answer 2

Answer:

10

Explanation:

2ab=(a2+b2)-(a2-b2)

29-9=20

=>ab=10