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If a- b= 7 and (a)2 +(b)2 = 85 ,find (a)3 - (b)3.

Posted by Prerna Sinha 4 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 4 years, 10 months ago

a-b=7 ⇒a=7+b .....(i)
a²+b²=85 ....(ii)

Substitution of equation 1 to equation 2.
(7+b)²+b² =85
49+14b +b²+b² =85
2b²+14b-36 =0
b² +7b -18 =0
(b+9)(b-2) =0
b=-9 v b=2

Find value of a
a-b=7
⇒if b=-9
a-(-9)=7
a =7-9
=-2
⇒if b=2
a-2=7
a = 7+2
=9

So value of a³ - b³ there are 2 options
⇒if (a,b) = (-2,-9)
a³-b³ = -2³ - (-9)³
= -8 +729
= 721

⇒if (a,b) = (2,9)
a³-b³ = 2³ - 9³
= 8-729
= -721

0Thank You

ANSWER

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