A + b is equal to 5, a square + b square is equal to 11 kama prove that a cube plus b cube is equal to 20
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Hello Mate!
a + b = 5 ( Given ) __(i)
a² + b² = 11 ( Given )
Squaring equation (i)
( a + b )² = 5²
a² + b² + 2ab = 25
11 + 2ab = 25
2ab = 14 => ab = 7
now, a³ + b³ = ( a + b )( a² + b² - ab )
Now substituting values we get,
20 = ( 5 )( 11 - 7 )
20 = 5 × 4 = 20
Hence value if a³ + b³ is 20.
Therefore proved.
Have great future ahead!
a + b = 5 ( Given ) __(i)
a² + b² = 11 ( Given )
Squaring equation (i)
( a + b )² = 5²
a² + b² + 2ab = 25
11 + 2ab = 25
2ab = 14 => ab = 7
now, a³ + b³ = ( a + b )( a² + b² - ab )
Now substituting values we get,
20 = ( 5 )( 11 - 7 )
20 = 5 × 4 = 20
Hence value if a³ + b³ is 20.
Therefore proved.
Have great future ahead!
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