\sqrt { 3 } x ^ { 2 } + 7 x + 2 \sqrt { 3 }
factorisation
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Class 10
>>Maths
>>Quadratic Equations
>>Solutions of Quadratic Equations
>>√(3x^2-7x-30) - √(2x^2-7x-5...
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3x
2
−7x−30
−
2x
2
−7x−5
=x−5
Medium
Solution
verified
Verified by Toppr
3x
2
−7x−30
−
2x
2
−7x−5
=x−5
3x
2
−7x−30
=x−5+
2x
2
−7x−5
3x
2
−7x−30
2
=x−5+
2x
2
−7x−5
2
by squaring both sides
⇒3x
2
−7x−30=(x−5)
2
+2x
2
−7x−5+2(x−5)
(2x
2
−7x−5)
⇒3x
2
−7x−30=x
2
−10x+25+2x
2
−7x−5+2(x−5)
(2x
2
−7x−5)
⇒3x
2
−7x−30=3x
2
−17x+20+2(x−5)
(2x
2
−7x−5)
⇒−7x+17x−30−20=2(x−5)
(2x
2
−7x−5)
⇒10x−50=2(x−5)
(2x
2
−7x−5)
⇒10(x−5)=2(x−5)
(2x
2
−7x−5)
⇒5=
(2x
2
−7x−5)
⇒25=2x
2
−7x−5 by squaring on both sides
⇒2x
2
−7x−5−25=0
⇒2x
2
−7x−30=0
⇒(2x+5)(x−6)=0 on factorising
∴x=
2
−5
,6
For x=
2
−5
the
3x
2
−7x−30
−
2x
2
−7x−5
=x−5 equation becomes
3(
2
−5
)
2
−7×
2
−5
−30
−
2(
2
−5
)
2
−7×
2
−5
−5
=
2
−5
−5
=
4
75
+
2
35
−30
−
2×
4
25
+
2
35
−5
=
4
145−120
−
2
40
=
4
25
−
20
=
2
5
−4
5
= RHS
∵x−5=
2
−5
−5=
2
−15
Hence x=
2
−5
is not a solution
For x=6 the
3x
2
−7x−30
−
2x
2
−7x−5
=x−5 equation becomes
3(6)
2
−7×6−30
−
2(6)
2
−7×6−5
=6−5
=
108−72
−
72−47
=1
=
36
−
25
=6−5=1
Thus, x=6 is the only solution for the above equation