If a + b = 5 and a - b = 4, find a2+ b2 and ab.
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ANSWER
THIS IS CORRECT ANSWER
a+b=5
On squaring both sides,
(a+b)^2=(5)^2
=> a^2+2ab+b^2=25…………………….(1)
a-b=4
On squaring both sides,
(a-b)^2=(4)^2
=a^2–2ab+b^2=16……………..………….(2)
Adding equation (1) and (2), we get,
(a^2+2ab+b^2)+(a^2–2ab+b^2)=25+16
=> a^2+2ab+b^2+a^2–2ab+b^2=41
=> a^2+a^2+b^2+b^2+2ab-2ab=41
=> 2a^2+2b^2=41
=> 2(a^2+b^2)=41
=> a^2+b^2=41/2
=>a^2+b^2=20.5
Hence, a^2+b^2=20.5 .
HOPE THIS HELPS YOU
Answered by
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Answer:
a+b = 5
a-b=4 so a = 9/2 and b = 1/2
a^2 + b^2
(9/2)^2 + (1/2)^2
81/4 + 1/4
82/4
41/2
so a^2 + b^2 = 41/2
use a+ b whole square for find ab
(a+b)^2 = a^2+b^2 +2ab
put the values..
25 = 41/2 + 2ab
25 = 20.5 + 2ab
ab = 4.5/2
ab = 2.25..
or u can find ab by simply multiplying a x b
as we have find it earlier...
hope this will help you..
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