Factorise the expression
mx³y - nxy³ + 2mx² - 2ny²
D=(mx−5)2−4(3)(2x2−2)=m2x2+25−10mx−24x2+24=x2(m2−24)−10mx+49=(m2−24)x2−2.7.75.mx+72
the above expression will be a perfect square when
(2.7.75m)2=4×(m2−24)×49⇒100m2=49×4(m2−24)⇒25m2=49(m2−24)⇒4925m2=m2−24⇒m2=4925m2+24⇒4925m2=24⇒m2=49⇒m=±7
the above expression will be a perfect square when
(2.7.75m)2=4×(m2−24)×49⇒100m2=49×4(m2−24)⇒25m2=49(m2−24)⇒4925m2=m2−24⇒m2=4925m2+24⇒4925m2=24⇒m2=49⇒m=±7
Answers
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Step-by-step explanation:
2x
2
+mxy+3y
2
−5y−2 has two rational factors
⇒ it can be factorized into two linear factors
let's write it as a quadratic in y
3y
2
+y(mx−5)+2x
2
−2 -(i)
Since it has two factors.
⇒ the discriminant of the equation (i) should be perfect square.
D=(mx−5)
2
−4(3)(2x
2
−2)
=m
2
x
2
+25−10mx−24x
2
+24
=x
2
(m
2
−24)−10mx+49
=(m
2
−24)x
2
−2.7.
7
5
.mx+7
2
the above expression will be a perfect square when
(2.7.
7
5
m)
2
=4×(m
2
−24)×49
⇒100m
2
=49×4(m
2
−24)
⇒25m
2
=49(m
2
−24)
⇒
49
25
m
2
=m
2
−24
⇒m
2
=
49
25
m
2
+24
⇒
49
25m
2
=24
⇒m
2
=49
⇒m=±7
Similar questions
2x2+mxy+3y2−5y−2 has two rational factors
⇒ it can be factorized into two linear factors
let's write it as a quadratic in y
3y2+y(mx−5)+2x2−2 -(i)
Since it has two factors.
⇒ the discriminant of the equation (i) should be perfect square.