









Subscribe to our Youtube Channel - https://you.tube/teachoo
Last updated at Dec. 24, 2018 by Teachoo
Transcript
Ex 9.5, 4 Simplify. (i) (π^2βπ^2 )^2 (π^2βπ^2 )^2 (π₯βπ¦)^2=π₯^2+π¦^2β2π₯π¦ Putting π₯ = π^2 & π¦ = π^2 = (π^2 )^2+(π^2 )^2β2(π^2 )(π^2 ) = π^(2 Γ 2)+π^(2 Γ 2)β2π^2 π^2 = π^π+π^πβππ^π π^π Ex 9.5, 4 Simplify. (ii) (2π₯+5)^2β(2π₯β5)^2 Solving (ππ+π)^π (π+π)^2=π^2+π^2+2ππ Putting π = 2π₯ & π = 5 = (2π₯)^2+(5)^2+2(2π₯)(5) = 4π₯^2+25+20π₯ Solving (ππβπ)^π (πβπ)^2=π^2+π^2β2ππ Putting π = 2π₯ & π = 5 = (2π₯)^2+(5)^2β2(2π₯)(5) = 4π₯^2+25β20π₯ = 4π₯^2+25+20π₯β4π₯^2β25+20π₯ = (4π₯^2β4π₯^2 )+(25β25)+(20π₯+20π₯) = 0+0+40π₯ = πππ Ex 9.5, 4 Simplify. (iii) (7πβ8π)^2+(7π+8π)^2 Solving (ππβππ)^π (πβπ)^2=π^2+π^2β2ππ Putting π = 7π & π = 8π = (7π)^2+(8π)^2β2(7π)(8π) = 49π^2+64π^2β(14Γ8)ππ = 49π^2+64π^2β112ππ Solving (ππ+ππ)^π (π+π)^2=π^2+π^2+2ππ Putting π = 7π & π = 8π = (7π)^2+(8π)^2+2(7π)(8π) = 49π^2+64π^2+(14Γ8)ππ = 49π^2+64π^2+112ππ β΄ (7πβ8π)^2+(7π+8π)^2 = (49π^2+64π^2β112ππ)+(49π^2+64π^2+112ππ) = (49π^2+49π^2 )+(64π^2+64π^2 )+(β112ππ+112ππ) = πππ^π+ππππ^π Ex 9.5, 4 Simplify. (iv) (4π+5π)^2+(5π+4π)^2 Solving (ππ+ππ)^π (π+π)^2=π^2+π^2+2ππ Putting π = 4π & π = 5π = (4π)^2+(5π)^2+2(4π)(5π) = 16π^2+25π^2+40ππ Solving (ππ+ππ)^π (π+π)^2=π^2+π^2+2ππ Putting π = 5π & π = 4π = (5π)^2+(4π)^2+2(5π)(4π) = 25π^2+16π^2+40ππ β΄ (4π+5π)^2+(5π+4π)^2 = (16π^2+25π^2+40ππ)+(25π^2+16π^2+40ππ) = (16π^2+25π^2 )+(25π^2+16π^2 )+(40ππ+40ππ) = πππ^π+πππ^π+ππππ Ex 9.5, 4 Simplify. (v) (2.5πβ1.5π)^2 β(1.5πβ2.5π)^2 Solving (π.ππβπ.ππ)^π (πβπ)^2=π^2+π^2β2ππ Putting π = 2.5π & π = 1.5π = (2.5π)^2+(1.5π)^2β 2(2.5π)(1.5π) = (γ2.5γ^2Γπ^2 )+(γ1.5γ^2Γπ)^2 β (2Γ2.5Γ1.5)Γ(πΓπ) = (25/10)^2 π^2+(15/10)^2 π^2 β (2Γ25/10Γ15/10)ππ = 625/100 π^2+225/100 π^2β750/100 ππ Solving (π.ππβπ.ππ)^π (πβπ)^2=π^2+π^2β2ππ Putting π = 1.5π & π = 2.5π = (1.5π)^2+(2.5π)^2β2(1.5π)(2.5π) = (γ1.5γ^2Γπ^2 )+(γ2.5γ^2Γπ)^2β(2Γ1.5Γ2.5)Γ(πΓπ) = (15/10)^2 π^2+(25/10)^2 π^2β(2Γ15/10Γ25/10)ππ = 225/100 π^2+625/100 π^2β750/100 ππ β΄ (2.5πβ1.5π)^2 β(1.5πβ2.5π)^2 = 625/100 π^2+225/100 π^2β750/100 ππβ(225/100 π^2+625/100 π^2β750/100 ππ" " ) = 625/100 π^2+225/100 π^2β750/100 ππβ225/100 π^2β625/100 π^2+750/100 ππ = (625/100β225/100) π^2+(225/100β625/100) π^2+(β750/100 +750/100)ππ = 400/100 π^2β400/100 π^2 = ππ^πβππ^π Ex 9.5, 4 Simplify. (vi) (ππ+ππ)^2β2ππ^2 π (ππ+ππ)^2β2ππ^2 π (π₯+π¦)^2=π₯^2+π¦^2+2π₯π¦ Putting π₯ = ππ & π¦ = ππ = (ππ)^2+(ππ)^2+2(ππ)(ππ)β2ππ^2 π = (π^2Γπ^2 )+(π^2Γπ^2 )+(2ΓπΓ(πΓπ)Γπ)β2ππ^2 π = π^2 π^2+π^2 π^2+2ππ^2 πβ2ππ^2 π = π^π π^π+π^π π^π Ex 9.5, 4 Simplify. (vii) (π^2βπ^2 π)^2+2π^3 π^2 (π^2βπ^2 π)^2+2π^3 π^2 (πβπ)^2=π^2+π^2β2ππ Putting π = π^2 & π = π^2 π = (π^2 )^2+(π^2 π)^2β2(π^2 )(π^2 π)+2π^3 π^2 = π^(2 Γ 2)+(π^2 )^2Γπ^2β2Γ(π^2Γπ)Γπ^2+2π^3 π^2 = π^4+π^4 π^2β2π^3 π^2+2π^3 π^2 = π^π+π^π π^π
About the Author