two numbers that multiply to 16 and add up to 24
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β+α = 24
βα = 16
x² - 24 x + 16 =0
α, β = ( 24 +- √[24² -64] ) /2 = 12 +- 8√2
α = 12 + 8√2
β = 12 - 8√2
βα = 16
x² - 24 x + 16 =0
α, β = ( 24 +- √[24² -64] ) /2 = 12 +- 8√2
α = 12 + 8√2
β = 12 - 8√2
kvnmurty:
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What is a,b
α, β = (24 ..... this is the solution to the quadratic equation..
otherwise: do as follows:
a + b = 24 a b = 16
(a -b)² = (a +b)² - 4 a b = 24² - 4*16 = 512
a - b = + √512 or - √512 or,
= + 16√2 or - 16 √2
add a+b + a - b = 2a = 24 + 16 √2 => a = 12 + 8 √2
so b = 12 - 8 √2
Okay Now...
(a -b)² = (a +b)² - 4 a b = 24² - 4*16 = 512
a - b = + √512 or - √512 or,
= + 16√2 or - 16 √2
add a+b + a - b = 2a = 24 + 16 √2 => a = 12 + 8 √2
so b = 12 - 8 √2
Okay Now...
yes
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