(7+z)(9-z)+(7-z)(9+z)=76 eching

$$( 7 + z ) ( 9 - z ) + ( 7 - z ) ( 9 + z ) = 76$$

z uchun yechish

$$z=5$$

$$z=-5$$

Kvadrat ildizini topish bo'yicha qadamlar

7+z ga 9-z ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$63+2z-z^{2}+\left(7-z\right)\left(9+z\right)=76$$

7-z ga 9+z ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$63+2z-z^{2}+63-2z-z^{2}=76$$

126 olish uchun 63 va 63'ni qo'shing.

$$126+2z-z^{2}-2z-z^{2}=76$$

0 ni olish uchun 2z va -2z ni birlashtirish.

$$126-z^{2}-z^{2}=76$$

-2z^{2} ni olish uchun -z^{2} va -z^{2} ni birlashtirish.

$$126-2z^{2}=76$$

Ikkala tarafdan 126 ni ayirish.

$$-2z^{2}=76-126$$

-50 olish uchun 76 dan 126 ni ayirish.

$$-2z^{2}=-50$$

Ikki tarafini -2 ga bo‘ling.

$$z^{2}=\frac{-50}{-2}$$

25 ni olish uchun -50 ni -2 ga bo‘ling.

$$z^{2}=25$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$z=5 z=-5$$

Kvadrat tenglamalaridan foydalanish qoidalari

7+z ga 9-z ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$63+2z-z^{2}+\left(7-z\right)\left(9+z\right)=76$$

7-z ga 9+z ni ko‘paytirish orqali distributiv xususiyatdan foydalaning va ifoda sifatida birlashtiring.

$$63+2z-z^{2}+63-2z-z^{2}=76$$

126 olish uchun 63 va 63'ni qo'shing.

$$126+2z-z^{2}-2z-z^{2}=76$$

0 ni olish uchun 2z va -2z ni birlashtirish.

$$126-z^{2}-z^{2}=76$$

-2z^{2} ni olish uchun -z^{2} va -z^{2} ni birlashtirish.

$$126-2z^{2}=76$$

Ikkala tarafdan 76 ni ayirish.

$$126-2z^{2}-76=0$$

50 olish uchun 126 dan 76 ni ayirish.

$$50-2z^{2}=0$$

Bu kabi kvadrat tenglamalarni x^{2} sharti bilan, biroq x shartisiz hamon kvadrat tenglamasidan foydalanib yechish mumkin, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ular standart formulaga solingandan so'ng: ax^{2}+bx+c=0.

$$-2z^{2}+50=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} -2 ni a, 0 ni b va 50 ni c bilan almashtiring.

$$z=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 50}}{2\left(-2\right)}$$

0 kvadratini chiqarish.

$$z=\frac{0±\sqrt{-4\left(-2\right)\times 50}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$z=\frac{0±\sqrt{8\times 50}}{2\left(-2\right)}$$

8 ni 50 marotabaga ko'paytirish.

$$z=\frac{0±\sqrt{400}}{2\left(-2\right)}$$

400 ning kvadrat ildizini chiqarish.

$$z=\frac{0±20}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$z=\frac{0±20}{-4}$$

z=\frac{0±20}{-4} tenglamasini yeching, bunda ± musbat. 20 ni -4 ga bo'lish.

$$z=-5$$

z=\frac{0±20}{-4} tenglamasini yeching, bunda ± manfiy. -20 ni -4 ga bo'lish.

$$z=5$$

Tenglama yechildi.

$$z=-5 z=5$$