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प्रश्न
If a - b = 0.9 and ab = 0.36; find:
(i) a + b
(ii) a2 - b2.
उत्तर
(i) We know that,
( a - b )2 = a2 - 2ab + b2
and
( a + b )2 = a2 + 2ab + b2
Rewrite the above equation, we have
( a + b )2 = a2 + b2 - 2ab + 4ab
= ( a - b )2 + 4ab ...(1)
Given that a - b = 0.9 ; ab = 0.36
Substitute the values of ( a - b ) and (ab)
in equation (1), we have
( a + b )2 = ( 0.9 )2 + 4( 0.36 )
= 0.81 + 1.44 = 2.25
⇒ a + b = `+- sqrt2.25`
⇒ a + b = `+-1.5` ..(2)
(ii) We know that,
a2 - b2 = ( a + b )( a - b ) ....(3)
From equation (2) we have,
a + b = `+-`1.5
Thus equation (3) becomes,
a2 - b2 = `(+- 1.5)(0.9)` [ given a - b = 0.9 ]
⇒ a2 - b2 = `+-`1.35
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